Irreducible morphisms of categories of complexes

We study irreducible morphisms of complexes. In particular, we show that the irreducible morphisms having one (finite) irreducible submorphism fall into three canonical forms and we give necessary and sufficient conditions for a given morphism of that type to be irreducible. Our characterization of the above mentioned type of irreducible morphisms of complexes characterizes also some class of irreducible morphisms of the derived category D(-)(A) for A a finite dimensional k-algebra, where k is a field. (C) 2009 Published by Elsevier Inc.

A NOTE ON THE COMPOSITE OF TWO IRREDUCIBLE MORPHISMS

In this note, we show that a composite of two irreducible morphisms between indecomposable modules cannot lie in R(3)\R(5).

On the composite of irreducible morphisms in almost sectional paths

We study here when the composite of it irreducible morphisms in almost sectional paths is non-zero and lies in Rn+1 (C) 2007 Elsevier B.V. All rights reserved.

ON THE COMPOSITE OF THREE IRREDUCIBLE MORPHISMS IN THE FOURTH POWER OF THE RADICAL

We study here the nonzero composite of three irreducible morphisms between indecomposable modules lying in the fourth power of the radical.

Symmetry breaking in the genetic code: Finite groups

We investigate the possibility of interpreting the degeneracy of the genetic code, i.e., the feature that different codons (base triplets) of DNA are transcribed into the same amino acid, as the result of a symmetry breaking process, in the context of finite groups. In the first part of this paper, we give the complete list of all codon representations (64-dimensional irreducible representations) of simple finite groups and their satellites (central extensions and extensions by outer automorphisms). In the second part, we analyze the branching rules for the codon representations found in the first part by computational methods, using a software package for computational group theory. The final result is a complete classification of the possible schemes, based on finite simple groups, that reproduce the multiplet structure of the genetic code. (C) 2010 Elsevier Ltd. All rights reserved.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras

We address two problems with the structure and representation theory of finite W-algebras associated with general linear Lie algebras. Finite W-algebras can be defined using either Kostant`s Whittaker modules or a quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of finite W-algebras. The second main result is a parameterization of finite families of irreducible Gelfand-Tsetlin modules using Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand-Tsetlin modules for finite W-algebras. (C) 2009 Elsevier Inc. All rights reserved.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.