Related papers: Extended affine Weyl groups: Presentation by conju…
We obtain a presentation of certain affine q-Schur algebras in terms of generators and relations. The presentation is obtained by adding more relations to the usual presentation of the quantized enveloping algebra of type affine gl_n. Our…
This paper is motivated by several combinatorial actions of the affine Weyl group of type $C_n$. Addressing a question of David Vogan, it was shown in an earlier paper that these permutation representations are essentialy…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
We apply the method of iterated inflations to show that the wreath product of a cellular algebra with a symmetric group is cellular, and obtain descriptions of the cell and simple modules together with a semisimplicity condition for such…
We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…
Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
We study the category of finite--dimensional bi--graded representations of toroidal current algebras associated to finite--dimensional complex simple Lie algebras. Using the theory of graded representations for current algebras, we…
In this paper we first determine all irreducible representations of a wedge product of two table algebras in terms of the irreducible representations of two factors involved. Then we give some necessary and sufficient conditions for a table…
This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…
In this paper, we study length categories using iterated extensions. We consider the problem of classifying all indecomposable objects in a length category, and the problem of characterizing those length categories that are uniserial. We…
Let W be a Weyl group. We introduce the notion of positive conjugacy class in W. This generalizes the notion of regular elliptic conjugacy class in the sense of Springer.
We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…
Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric properties. Using recent structural results of Mili\'cevi\'c,…
We give a birational realization of affine Weyl group of type $A^{(1)}_{m-1} \times A^{(1)}_{n-1}$. We apply this representation to construct some discrete integrable systems and discrete Painlev\'e equations. Our construction has a…
In 1990, D.Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow's algorithm is designed for computation of weights, $W$-orbits and elements of the Weyl group. An extension of Snow's algorithm is…
We introduce a class of non-commutative algebras that carry a non-commutative (geometric) cluster structure which are generated by identical copies of generalized Weyl algebras. Equivalent conditions for the finiteness of the set of the…
We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory of nonsymmetric Macdonald polynomials. As an application we…
We show that the irreducible representation of the asymptotic Hecke algebra corresponding to a special representation of a Weyl group admits a basis with strong positivity properties.
The problem of classifying equivalence classes of presentations up to isomorphism of Cayley graphs is considered in this article in the case of dicyclic groups. The number of equivalence classes of presentations is uniformly bounded - it is…