On a Question of Kulshammer for Representations of Finite Groups in Reductive Groups

Peer reviewed

On a Question of Kulshammer for Representations of Finite Groups in Reductive Groups

Peer reviewed

Quotients d'une variété algébrique par un groupe algébrique linéairement réductif et ses sous-groupes maximaux unipotents

La construction d'un quotient, en topologie, est relativement simple; si $G$ est un groupe topologique agissant sur un espace topologique $X$, on peut considérer l'application naturelle de $X$ dans $X/G$, l'espace d'orbites muni de la topologie quotient. En géométrie algébrique, malheureusement, il n'est généralement pas possible de munir l'espace d'orbites d'une structure de variété. Dans le cas de l'action d'un groupe linéairement réductif $G$ sur une variété projective $X$, la théorie géométrique des invariants nous permet toutefois de construire un morphisme de variété d'un ouvert $U$ de $X$ vers une variété projective $X//U$, se rapprochant autant que possible d'une application quotient, au sens topologique du terme. Considérons par exemple $X\subseteq P^{n}$, une $k$-variété projective sur laquelle agit un groupe linéairement réductif $G$ et supposons que cette action soit induite par une action linéaire de $G$ sur $A^{n+1}$. Soit $\widehat{X}\subseteq A^{n+1}$, le cône affine au dessus de $\X$. Par un théorème de la théorie classique des invariants, il existe alors des invariants homogènes $f_{1},...,f_{r}\in C[\widehat{X}]^{G}$ tels que $$C[\widehat{X}]^{G}= C[f_{1},...,f_{r}].$$ On appellera le nilcone, que l'on notera $N$, la sous-variété de $\X$ définie par le locus des invariants $f_{1},...,f_{r}$. Soit $Proj(C[\widehat{X}]^{G})$, le spectre projectif de l'anneau des invariants. L'application rationnelle $$\pi:X\dashrightarrow Proj(C[f_{1},...,f_{r}])$$ induite par l'inclusion de $C[\widehat{X}]^{G}$ dans $C[\widehat{X}]$ est alors surjective, constante sur les orbites et sépare les orbites autant qu'il est possible de le faire; plus précisément, chaque fibre contient exactement une orbite fermée. Pour obtenir une application régulière satisfaisant les mêmes propriétés, il est nécessaire de jeter les points du nilcone. On obtient alors l'application quotient $$\pi:X\backslash N\rightarrow Proj(C[f_{1},...,f_{r}]).$$ Le critère de Hilbert-Mumford, dû à Hilbert et repris par Mumford près d'un demi-siècle plus tard, permet de décrire $N$ sans connaître les $f_{1},...,f_{r}$. Ce critère est d'autant plus utile que les générateurs de l'anneau des invariants ne sont connus que dans certains cas particuliers. Malgré les applications concrètes de ce théorème en géométrie algébrique classique, les démonstrations que l'on en trouve dans la littérature sont généralement données dans le cadre peu accessible des schémas. L'objectif de ce mémoire sera, entre autres, de donner une démonstration de ce critère en utilisant autant que possible les outils de la géométrie algébrique classique et de l'algèbre commutative. La version que nous démontrerons est un peu plus générale que la version originale de Hilbert \cite{hilbert} et se retrouve, par exemple, dans \cite{kempf}. Notre preuve est valide sur $C$ mais pourrait être généralisée à un corps $k$ de caractéristique nulle, pas nécessairement algébriquement clos. Dans la seconde partie de ce mémoire, nous étudierons la relation entre la construction précédente et celle obtenue en incluant les covariants en plus des invariants. Nous démontrerons dans ce cas un critère analogue au critère de Hilbert-Mumford (Théorème 6.3.2). C'est un théorème de Brion pour lequel nous donnerons une version un peu plus générale. Cette version, de même qu'une preuve simplifiée d'un théorème de Grosshans (Théorème 6.1.7), sont les éléments de ce mémoire que l'on ne retrouve pas dans la littérature.

Le théorème de Borel-Weil-Bott

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Classical Invariants for Principal Series and Isomorphisms of Root Data

We develop some new techniques to calculate the Schur indicator for self-dual irreducible Langlands quotients of the principal series representations. Using these techniques we derive some new formulas for the Schur indicator and the real-quaternionic indicator. We make progress towards developing an algorithm to decide whether or not two root data are isomorphic. When the derived group has cyclic center, we solve the isomorphism problem completely. An immediate consequence is a clean and precise classification theorem for connected complex reductive groups whose derived groups have cyclic center.

Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

Design, Synthesis And Biological Evaluation Of Hybrid Bioisoster Derivatives Of N-acylhydrazone And Furoxan Groups With Potential And Selective Anti-trypanosoma Cruzi Activity.

Hybrid bioisoster derivatives from N-acylhydrazones and furoxan groups were designed with the objective of obtaining at least a dual mechanism of action: cruzain inhibition and nitric oxide (NO) releasing activity. Fifteen designed compounds were synthesized varying the substitution in N-acylhydrazone and in furoxan group as well. They had its anti-Trypanosoma cruzi activity in amastigotes forms, NO releasing potential and inhibitory cruzain activity evaluated. The two most active compounds (6, 14) both in the parasite amastigotes and in the enzyme contain the nitro group in para position of the aromatic ring. The permeability screening in Caco-2 cell and cytotoxicity assay in human cells were performed for those most active compounds and both showed to be less cytotoxic than the reference drug, benznidazole. Compound 6 was the most promising, since besides activity it showed good permeability and selectivity index, higher than the reference drug. Thereby the compound 6 was considered as a possible candidate for additional studies.

Comparative Cytogenetics Of Physalaemus albifrons And Physalaemus Cuvieri Species Groups (anura, leptodactylidae).

Recently, Physalaemus albifrons (Spix, 1824) was relocated from the Physalaemus cuvieri group to the same group as Physalaemus biligonigerus (Cope, 1861), Physalaemus marmoratus (Reinhardt & Lütken, 1862) and Physalaemus santafecinus Barrio, 1965. To contribute to the analysis of this proposition, we studied the karyotypes of Physalaemus albifrons, Physalaemus santafecinus and three species of the Physalaemus cuvieri group. The karyotype of Physalaemus santafecinus was found to be very similar to those of Physalaemus biligonigerus and Physalaemus marmoratus, which were previously described. A remarkable characteristic that these three species share is a conspicuous C-band that extends from the pericentromeric region almost to the telomere in the short arm of chromosome 3. This characteristic is not present in the Physalaemus albifrons karyotype and could be a synapomorphy of Physalaemus biligonigerus, Physalaemus marmoratus and Physalaemus santafecinus. The karyotype of Physalaemus santafecinus is also similar to those of Physalaemus marmoratus and Physalaemus biligonigerus owing to the presence of several terminal C-bands and the distal localization of the NOR in a small metacentric chromosome. In contrast, the Physalaemus albifrons karyotype has no terminal C-bands and its NOR is located interstitially in the long arm of submetacentric chromosome 8. The NOR-bearing chromosome of Physalaemus albifrons very closely resembles those found in Physalaemus albonotatus (Steindachner, 1864), Physalaemus cuqui Lobo, 1993 and some populations of Physalaemus cuvieri Fitzinger, 1826. Additionally, the Physalaemus albifrons karyotype has an interstitial C-band in chromosome 5 that has been exclusively observed in species of the Physalaemus cuvieri group. Therefore, we were not able to identify any chromosomal feature that supports the reallocation of Physalaemus albifrons.

Metacommunity Versus Biogeography: A Case Study Of Two Groups Of Neotropical Vegetation-dwelling Arthropods.

Biogeography and metacommunity ecology provide two different perspectives on species diversity. Both are spatial in nature but their spatial scales do not necessarily match. With recent boom of metacommunity studies, we see an increasing need for clear discrimination of spatial scales relevant for both perspectives. This discrimination is a necessary prerequisite for improved understanding of ecological phenomena across scales. Here we provide a case study to illustrate some spatial scale-dependent concepts in recent metacommunity studies and identify potential pitfalls. We presented here the diversity patterns of Neotropical lepidopterans and spiders viewed both from metacommunity and biogeographical perspectives. Specifically, we investigated how the relative importance of niche- and dispersal-based processes for community assembly change at two spatial scales: metacommunity scale, i.e. within a locality, and biogeographical scale, i.e. among localities widely scattered along a macroclimatic gradient. As expected, niche-based processes dominated the community assembly at metacommunity scale, while dispersal-based processes played a major role at biogeographical scale for both taxonomical groups. However, we also observed small but significant spatial effects at metacommunity scale and environmental effects at biogeographical scale. We also observed differences in diversity patterns between the two taxonomical groups corresponding to differences in their dispersal modes. Our results thus support the idea of continuity of processes interactively shaping diversity patterns across scales and emphasize the necessity of integration of metacommunity and biogeographical perspectives.

Cephalometric And Anthropometric Data Of Obstructive Apnea In Different Age Groups.

Patients with obstructive sleep apnea syndrome usually present with changes in upper airway morphology and/or body fat distribution, which may occur throughout life and increase the severity of obstructive sleep apnea syndrome with age. To correlate cephalometric and anthropometric measures with obstructive sleep apnea syndrome severity in different age groups. A retrospective study of cephalometric and anthropometric measures of 102 patients with obstructive sleep apnea syndrome was analyzed. Patients were divided into three age groups (≥20 and <40 years, ≥40 and <60 years, and ≥60 years). Pearson's correlation was performed for these measures with the apnea-hypopnea index in the full sample, and subsequently by age group. The cephalometric measures MP-H (distance between the mandibular plane and the hyoid bone) and PNS-P (distance between the posterior nasal spine and the tip of the soft palate) and the neck and waist circumferences showed a statistically significant correlation with apnea-hypopnea index in both the full sample and in the ≥40 and <60 years age group. These variables did not show any significant correlation with the other two age groups (<40 and ≥60 years). Cephalometric measurements MP-H and PNS-P and cervical and waist circumferences correlated with obstructive sleep apnea syndrome severity in patients in the ≥40 and <60 age group.

Quality Of Life On Arterial Hypertension: Validity Of Known Groups Of Minichal.

Introductions: In the care of hypertension, it is important that health professionals possess available tools that allow evaluating the impairment of the health-related quality of life, according to the severity of hypertension and the risk for cardiovascular events. Among the instruments developed for the assessment of health-related quality of life, there is the Mini-Cuestionario of Calidad de Vida en la Hipertensión Arterial (MINICHAL) recently adapted to the Brazilian culture. Objective: To estimate the validity of known groups of the Brazilian version of the MINICHAL regarding the classification of risk for cardiovascular events, symptoms, severity of dyspnea and target-organ damage. Methods: Data of 200 hypertensive outpatients concerning sociodemographic and clinical information and health-related quality of life were gathered by consulting the medical charts and the application of the Brazilian version of MINICHAL. The Mann-Whitney test was used to compare health-related quality of life in relation to symptoms and target-organ damage. The Kruskal-Wallis test and ANOVA with ranks transformation were used to compare health-related quality of life in relation to the classification of risk for cardiovascular events and intensity of dyspnea, respectively. Results: The MINICHAL was able to discriminate health-related quality of life in relation to symptoms and kidney damage, but did not discriminate health-related quality of life in relation to the classification of risk for cardiovascular events. Conclusion: The Brazilian version of the MINICHAL is a questionnaire capable of discriminating differences on the health‑related quality of life regarding dyspnea, chest pain, palpitation, lipothymy, cephalea and renal damage.Fundamento: No cuidado ao hipertenso, é importante que o profissional de saúde disponha de ferramentas que possibilitem avaliar o comprometimento da qualidade de vida relacionada à saúde, de acordo com a gravidade da hipertensão e o risco para eventos cardiovasculares. Dentre os instrumentos criados para avaliação da qualidade de vida relacionada à saúde, destaca-se o Mini-Cuestionario de Calidad de Vida en la Hipertensión Arterial (MINICHAL), recentemente adaptado para a cultura brasileira. Objetivo: Estimar a validade de grupos conhecidos da versão brasileira do MINICHAL em relação à classificação de risco para eventos cardiovasculares, sintomas, intensidade da dispneia e lesões de órgãos-alvo. Métodos: Foram investigados 200 hipertensos em seguimento ambulatorial, cujos dados sociodemográficos, clínicos e de qualidade de vida relacionada à saúde foram obtidos por meio de consulta ao prontuário e da aplicação da versão brasileira do MINICHAL. O teste de Mann-Whitney foi utilizado para comparar qualidade de vida relacionada à saúde em relação aos sintomas e às lesões de órgãos-alvo. Teste de Kruskal-Wallis e ANOVA com transformação nos ranks foram empregados para comparar qualidade de vida relacionada à saúde em relação à classificação de risco para eventos cardiovasculares e intensidade da dispneia, respectivamente. Resultados: O MINICHAL discriminou qualidade de vida relacionada à saúde em relação aos sintomas e dano renal (lesões de órgãos-alvo), porém não discriminou qualidade de vida relacionada à saúde em relação à classificação de risco para eventos cardiovasculares. Conclusão: A versão brasileira do MINICHAL é um instrumento capaz de discriminar diferenças na qualidade de vida relacionada à saúde em relação aos sintomas de dispneia, precordialgia, palpitação, lipotímia, cefaleia e presença de dano renal.

Identification of family variables in parents' groups of children with epilepsy

OBJECTIVE: To verify the effectiveness of the support group in the identification of family variables linked to epilepsy. METHOD: Pre-test were applied to parents of 21 children with benign epilepsy of childhood recently diagnosed, from 5 to 15 years, who participated in the groups at HC/Unicamp. There was a presentation of an educational video, discussion and application of the post-test 1. After six months, the post-test 2 was applied. RESULTS: The beliefs were: fear of swallowing the tongue during the seizures (76.19%) and of a future mental disease (66.67%). Facing the epilepsy, fear and sadness appeared. 76.19% of the parents presented overprotection and 90.48%, expected a new seizure. In the post-test 1, the parents affirmed that the information offered had modified the beliefs. In the post-test 2, 80.95% didn't report great doubts about epilepsy and 90.48% considered their relationship with their children better. CONCLUSIONS: The demystification of beliefs supplied from the groups influenced the family positively, prevented behavior alterations and guaranteed effective care in the attendance to the child with epilepsy.

Permeability of different groups of maxillary teeth after 38% hydrogen peroxide internal bleaching

This study evaluated the influence of internal tooth bleaching with 38% hydrogen peroxide (H2O2) on the permeability of the coronal dentin in maxillary anterior teeth and premolars. Seventy teeth (14 per group) were used: central incisors (CI), lateral incisor (LI), canines (C), first premolars (1PM) and second premolars (2PM). Pulp chamber access and transversal sectioning at 2 mm from the cementoenamel junction were performed and the specimens were divided into 2 groups (n= 7): a) no treatment and b) bleaching with 38% H2O2. The bleaching agent was applied to the buccal surface and to the pulp chamber for 10 min. This procedure was repeated 3 times. The specimens were processed histochemically with copper sulfate and rubeanic acid, sectioned longitudinally, and digitalized in a scanner. The area of stained dentin was measured using Image Tool software. Data were analyzed statistically by ANOVA and Tukey's HSD test (?=0.05). There was statistically significant difference (p<0.001) among the untreated groups, CI (0.23 ± 0.26) having the lowest permeability and LI (10.14 ± 1.89) the highest permeability. Among the bleached groups, dentin permeability was increased in all groups of teeth except for 2PM. It may be concluded that bleaching with 38% H2O2 affected dentin permeability near the pulp chamber in maxillary anterior teeth and in first and second premolars.

Dentin permeability of the apical third in different groups of teeth

This ex vivo study evaluated dentin permeability of the root canal in the apical third of different human groups of teeth. Eighty teeth were used, 8 from each dental group: maxillary and mandibular central incisors, lateral incisors and canines, maxillary first premolars (buccal and palatal roots), mandibular first premolars, and maxillary and mandibular second premolars, totalizing 88 roots that were distributed in 11 groups. The root canals were instrumented, irrigated with 1% NaOCl and 15% EDTA. Roots were immersed in 10% copper sulfate for 30 min and then in 1% rubeanic acid alcohol solution for the same period; this chemical reaction reveals dentin permeability by the formation of copper rubeanate, which is a dark-colored compound. Semi-serial 100-µm-thick cross-sections were obtained from the apical third of the roots. Five sections of each apical third were washed, dehydrated, cleared and mounted on glass slides for examination under optical microscopy. The percentage of copper ion infiltration and the amount of tubular dentin were quantified by morphometric analysis. The penetration of copper ions in the apical third ranged from 4.60 to 16.66%. The mandibular central and lateral incisors presented the highest dentin permeability (16.66%), while the maxillary canines and mandibular second and first premolars presented the lowest dentin permeability (4.60%, 4.80% and 5.71%, respectively; p<0.001). The other teeth presented intermediate permeability. In conclusion, dye penetration into dentin tubules at the apical region is strongly dependent on the group of teeth evaluated.