Related papers: Kac-Moody Groups and Their Representations
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…
According to Letourmy and Vendramin, a representation of a skew brace is a pair of representations on the same vector space, one for the additive group and the other for the multiplicative group, that satisfies a certain compatibility…
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…
The theory of admissible modules over symmetrizable anisotropic Kac-Moody superalgebras, introduced by Kac and Wakimoto in late 80's, is a well-developed subject with many applications, including representation theory of vertex algebras.…
We consider the subalgebras of split real, non-twisted affine Kac-Moody Lie algebras that are fixed by the Chevalley involution. These infinite-dimensional Lie algebras are not of Kac-Moody type and admit finite-dimensional unfaithful…
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as…
We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.
In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.
We study actions of compact quantum groups on type I factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz' results concerning Peter-Weyl theory for…
We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is…
The representation theory of involutory (or 'maximal compact') subalgebras of infinite-dimensional Kac-Moody algebras is largely terra incognita, especially with regard to fermionic (double-valued) representations. Nevertheless, certain…
The geometry of symmetric spaces, polar actions, isoparametric submanifolds and spherical buildings is governed by spherical Weyl groups and simple Lie groups. A natural generalization of semisimple Lie groups are affine Kac-Moody groups as…
Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
Motivated by the Langlands program in representation theory, number theory and geometry, the theory of representations of a reductive $p$-adic group over a coefficient ring different from the field of complex numbers has been widely…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
In this paper, we construct a representation of loop group and derive the formula of the corresponding representation of the affine Kac-Moody algebra with level 1. And we also provide a concrete realization of Whittaker functionals in the…
We review the categorical representation of a Kac-Moody algebra on unipotent representations of finite unitary groups in non-defining characteristic given by the authors. Then, we extend this construction to finite reductive groups of types…
We provide some necessary details to several arguments appearing in our previous paper ``Canonical bases for quantum generalized Kac-Moody algebras''. We also make the link with some other work on the same subject.