Algebraic Bethe ansatz for the anisotropic supersymmetric U model

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=l)(L)C(4)(where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra U-q[gl(2\1)] and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2\1)]. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.

Eigenvalues of Casimir invariants for unitary irreps of Uq(gl(m vertical bar n))

A fully explicit formula for the eigenvalues of Casimir invariants for U-q(gl(m/n)) is given which applies to all unitary irreps. This is achieved by making some interesting observations on atypicality indices for irreps occurring in the tensor product of unitary irreps of the same type. These results have applications in the determination of link polynomials arising from unitary irreps of U-q(gl(m/n)).

Quantum Lie algebras, their existence, uniqueness and q-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules L-h(g) of the quantized enveloping algebras U-h(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g(h) independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras L-h(g) are isomorphic to an abstract quantum Lie algebra g(h). In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras L-h(g) associated to the same g are isomorphic, 2) the quantum Lie product of any Ch(B) is q-antisymmetric. We also describe a construction of L-h(g) which establishes their existence.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

Helminth parasite communities of the water-rat, Hydromys chrysogaster, from Queensland

The helminth fauna from 124 water-rats, Hydromys chrysogaster, collected from 33 localities in Queensland was analysed. A total of 45 species of helminths was found, comprising 2 acanthocephalans, 2 cestodes, 13 nematodes and 28 trematodes. The helminth community of the water-rats in the region north of latitude 18 degrees (far north) was different from that of water-rats south of 18 degrees (central); Sorensen's Index 45.8% similarity, whereas Holmes and Podesta's Index gave 32.1% similarity. Comparisons with data from water-rats from southern and Tasmanian regions showed that they were different from each other and from both Queensland regions. The helminth communities were characterised by high diversity, dominated by trematodes in the central and Tasmanian regions, but with nematodes becoming more prominent in the far northern and southern regions. No core or secondary species were found in the Queensland helminth communities, the southern community was suggestive of a bimodal distribution and the Tasmanian had two core species. A checklist of helminth species occurring in water-rats from eastern Australia is provided.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

Algebraic Bethe ansatz for integrable extended Hubbard models arising from supersymmetric group solutions

Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.

Integrable extended hubbard models with boundary Kondo impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

Twisted sl(3, C)(k)((2)) current algebra: free field representation and screening currents

Motivated by application of twisted current algebra in description of the entropy of Ads(3) black hole, we investigate the simplest twisted current algebra sl(3, c)(k)((2)). Free field representation of the twisted algebra, and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three (beta, gamma) pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented. (C) 2001 Published by Elsevier Science B.V.

A comparison of anterior adhesive areas and secretions in Troglocephalus rhinobatidis and Neoheterocotyle rhinobatidis (Monogenea : Monocotylidae) from the gills of the shovelnose ray, Rhinobatos typus (Rhinobatidae)

This study continues the collection of data on the anterior adhesive areas and secretions of monopisthocotylean monogenean (flatworm) parasites and begins an investigation of their phylogenetic usefulness. Here, two species of parasitic worms from an elasmobranch, Troglocephalus rhinobatidis (Monocotylidae: Dasybatotreminae) and Neoheterocotyle rhinobatidis (Monocotylidae: Heterocotylinae), are compared and contrasted. It has been suggested in recent literature that these two taxa are more closely related than is currently recognised. Our data support this view. Both species have multiple apertures on the ventral anterior margin through which adhesive is secreted. Two types of secretion exit from multiple adjacent duct endings terminating in each aperture: rod-shaped (S1) and spherical-shaped (S2) bodies. S1 bodies of both species show nano-banding of similar size and are membrane bound. Ultrastructure of the glands, ducts, duct endings and secreted adhesive is similar for both species, but aperture shape differs. Away from the adhesive areas, tegumental inclusions are found to differ between the two species and another, apparently non-adhesive, secretion is found in N. rhinobatidis.

The Relationships between West Nile and Kunjin Viruses

Until recently, West Nile (WN) and Kunjin (KUN) viruses were classified as distinct types in the Flavivirus genus. However, genetic and antigenic studies on isolates of these two viruses indicate that the relationship between them is more complex. To better define this relationship, we performed sequence analyses on 32 isolates of KUN virus and 28 isolates of WN virus from different geographic areas, including a WN isolate from the recent outbreak in New York. Sequence comparisons showed that the KUN virus isolates from Australia were tightly grouped but that the WN virus isolates exhibited substantial divergence and could be differentiated into four district groups. KUN virus isolates from Australia were antigenically homologous and distinct from the WN isolates and a Malaysian KUN virus. Our results suggest that KUN and WN viruses comprise a group of closely related viruses that can be differentiated into subgroups on the basis of genetic and antigenic analyses.