Related papers: The Garnir Relations for Weyl Groups

This note is an attempt to give an answer for the following old I.M. Gelfand's question: why some important problems of integral geometry (e.g., the Radon transform and others) are related to harmonic analysis on groups, but for other quite…

We describe a set of defining relations for automorphism groups of finitely generated free algebras of Nielsen-Schreier varieties. In particular, this gives a representation of the automorphism groups of free Lie algebras by generators and…

This is an introduction to the group algebras of the symmetric groups, written for a quarter-long graduate course. After recalling the definition of group algebras (and monoid algebras) in general, as well as basic properties of…

the program of Langlands is studied here on the basis of: a)new concepts of global class field theory related to the explicit construction of global class fields and of reciprocity laws; b)the representations of the reductive algebraic…

We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of…

We survey the theory of totally symmetric sets, with applications to homomorphisms of symmetric groups, braid groups, linear groups, and mapping class groups.

In a previous paper I have defined a new basis for the representation ring of a Weyl group. In this paper we show that the new basis is related to the standard basis by an upper triangular unipotent matrix. We also give a new…

The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group. We present this category, when the Weyl group is the symmetric group, in the language of planar diagrams with…

We relate character theory of the symmetric groups $S_{2n}$ and $S_{2n+1}$ with that of the hyperoctahedral group $B_n = ({\mathbb Z}/2)^n \rtimes S_n$, as part of the expectation that the character theory of reductive groups with diagram…

We establish a connection between constructible representations (arising in the study of left cells in Weyl groups) and Catalan numbers.

We give a presentation of Feynman categories from a representation--theoretical viewpoint. Feynman categories are a special type of monoidal categories and their representations are monoidal functors. They can be viewed as a far reaching…

This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…

The power of the overlap formalism is illustrated by regularizing theories based on Majorana-Weyl fermions.

We give a characterization of connected solvable groups in terms of the existence of representations with certain geometric properties. The existence of such representations for the group of upper triangular matrices played an important…

The aim of this paper is to establish a pseudo-differential Weyl calculus on graded nilpotent Lie groups $G$ which extends the celebrated Weyl calculus on $\mathbb{R}^n$. To reach this goal, we develop a symbolic calculus for a very general…

In this paper we indicate one method of construction of linear representations of groups and algebras with translation invariant (except, maybe , finite number) defining relationships. As an illustration of this method, we give one approach…

This is a survey article on the Springer correspondence for symmetric spaces. We discuss various generalization of the theory of the Springer correspondence for reductive groups to symmetric spaces and exotic symmetric spaces associated to…

In this paper, we obtain relations in the Weyl groups of Kac-Moody algebras that come from mutation classes of skew-symmetrizable matrices. These relations generalize those obtained by Barot and Marsh for finite type. As an application, we…

We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…

Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For…