Related papers: Unipotent representations as a categorical centre

Let $G$ be a connected reductive group over $F_q$, where $q$ is large enough and the center of $G$ is connected. We are concerned with Lusztig's theory of {\em character sheaves}, a geometric version of the classical character theory of the…

Consider a Chevalley group over a finite field F_q such that the longest element in the Weyl group is central. In this paper we study the effect of changing q to -q in the polynomials which give the character values of unipotent…

In a recent paper I defined a new basis for the Grothendieck group of unipotent representations of an almost simple Chevalley group over a finite field. The definition for classical types was different from that for exceptional types. In…

Let G be any connected reductive group over a non-archimedean local field. We analyse the unipotent representations of G, in particular in the cases where G is ramified. We establish a local Langlands correspondence for this class of…

Let F be a non Archimedean locally compact field and let D be a central F-division algebra. We prove that any positive level supercuspidal irreducible representation of the group GL(m,D) is compactly induced from a representation of a…

We introduce the representation category $\mathscr{C}({\bf G})$ for a connected reductive algebraic group ${\bf G}$ which is defined over a finite field $\mathbb{F}_q$ of $q$ elements. We show that this category has many good properties for…

Let G(K) be the group of K-rational points of a connected adjoint simple algebraic group defined over a non-archimedean local field K. In this paper we classify the unipotent representations of G(K) in terms of the geometry of the Langlands…

After a brief review of recent rigorous results concerning the representation theory of rational chiral conformal field theories (RCQFTs) we focus on pairs (A,F) of conformal field theories, where F has a finite group G of global symmetries…

We show that every unitary representation of a solvable discrete virtually nilpotent group G is quasidiagonal. Roughly speaking, this says that every unitary representation of G approximately decomposes as a direct sum of finite dimensional…

We define a `nice representation' of a finitely presented group G as being a non-degenerate essentially surjective simplicial map f from a `nice' space X into a 3-complex associated to a presentation of G, with a strong control over the…

Cuspidal representations of a reductive p-adic group G over a field of characteristic different from p are relatively injective and projective with respect to extensions that split by a U-equivariant linear map for any subgroup U that is…

Let $F$ be a local non-archimedian field of positive characteristic, $D$ be a skew-field with center $F$ and $ G=D^{\star}$ be the multiplicative group of $D$. The goal of this paper is to provide a canonical decomposition of any complex…

The general linear group GL(n, K) over a field K contains a particularly prominent subgroup U(n, K), consisting of all the upper triangular unipotent elements. In this paper we are interested in the case when K is the finite field F_q, and…

Let $G$ be a connected reductive group defined over a finite field $\mathbb{F}_q$ of characteristic $p$, with Deligne--Lusztig dual $G^\ast$. We show that, over $\overline{\mathbb{Z}}[1/pM]$ where $M$ is the product of all bad primes for…

Let $G$ be a connected reductive algebraic group defined over the finite field $\FF_q$, where $q$ is a power of a good prime for $G$. We write $F$ for the Frobenius morphism of $G$ corresponding to the $\FF_q$-structure, so that $G^F$ is a…

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…

An approach to representations of finite groups is presented without recourse to character theory. Considering the group algebra C[G] as an algebra of linear maps on C[G] (by left multiplication), we derive the primitive central idempotents…

In this work, we analyze the structure of the category of partial representations of a finite group $G$ as a multifusion category, providing an alternative way to describe simple objects and their tensor products. We describe the…

In the paper we show that any irreducible representation of a finitely generated nilpotent group $G$ over a finitely generated field $F$ of characteristic zero is induced from a primitive representation of some subgroup of $G$.

Let K be a non-archimedean local field and let G be a connected reductive K-group which splits over an unramified extension of K. We investigate supercuspidal unipotent representations of the group G(K). We establish a bijection between the…