Related papers: The Garnir Relations for Weyl Groups

In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…

Let G be a connected reductive group. To any irreducible G-variety one associates a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We…

In this paper we define an equivalence relation on the set of all $x_{J}$ in order to form a basis for a new descent algebra of Weyl groups of type $A_{n}$. By means of this, we construct a new commutative and semi-simple descent algebra of…

Kantor pairs arise naturally in the study of 5-graded Lie algebras. In this article, we begin the study of simple Kantor pairs of arbitrary dimension. We introduce Weyl images of Kantor pairs and use them to construct examples of Kantor…

We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

Grassmannians are of fundamental importance in projective geometry, algebraic geometry, and representation theory. A vast literature has grown up utilizing using many different languages of higher mathematics, such as multilinear and tensor…

Let G be a simple reductive group over the complex numbers. Let W be the Weyl group of G. We propose a description of the Springer representations of W associated to various unipotent classes of G by a purely algebraic method involving the…

This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.

In the present article the existence of the Weyl representation for the canonical commutation relations algebras was proved in a Krein space.

We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

It is known that the Weyl families corresponding to unitary boundary pairs $(\mathcal{H},\Gamma)$ belong to the class $\tilde{\mathcal{R}}(\mathcal{H})$ of Nevanlinna families. Here we extend the theorem to the case of essentially unitary…

Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures and preferred connections are introduced…

We establish a relation between the known parametrization of a family of irreducible representations of a Weyl group and Springer's correspondence. We outline a parametrization of unipotent character sheaves on a connected reductive group…

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

Let W be a Weyl group. We define a new basis for the Grothendieck group of representations of W. This basis contains on the one hand the special representations of W and on the other hand the representations carried by the left cells of W.…

We obtain Schur-Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations.

Let g be a semisimple Lie algebra over the real numbers. We describe an explicit combinatorial construction of the real Weyl group of g with respect to a given Cartan subalgebra. An efficient computation of this Weyl group is important for…