Related papers: Unipotent representations as a categorical centre

We construct a model categorical equivalence between the category of simplicial vector spaces and the category of representations of a crossed simplicial group $\Delta G$ when each $G_n$ is finite and the characteristic of the ground field…

The category of finite dimensional (type 1) representations of a quantum affine algebra $U_q(\hat{{\mathfrak g}})$ is not semisimple. However, as any abelian category with finite-length objects, it admits a unique decomposition into a…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

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…

In this paper, we try to answer the following question: given a modular tensor category $\A$ with an action of a compact group $G$, is it possible to describe in a suitable sense the ``quotient'' category $\A/G$? We give a full answer in…

Motivated by recent advances in the categorification of quantum groups at prime roots of unity, we develop a theory of 2-representations for 2-categories enriched with a p-differential which satisfy finiteness conditions analogous to those…

We study the asymptotics of the reducible representations of the wreath products G\wr S_q=G^q \rtimes S_q for large q, where G is a fixed finite group and S_q is the symmetric group in q elements; in particular for G=Z/2Z we recover the…

Let $\text{U}(n,\mathbb{F}_{q^2})$ denote the subgroup of unitary matrices of the general linear group $\text{GL}(n,\mathbb{F}_{q^2})$ which fixes a Hermitian form and $M\geq 2$ an integer. This is a companion paper to the previous works…

Let F be a locally compact non-archimedean field, p its residue characteristic, and G a connected reductive group over F. Let C an algebraically closed field of characteristic p. We give a complete classification of irreducible admissible…

Let $\mathbb{F}_q$ be a finite field with $q$ elements, where $q$ is the power of an odd prime, and let $\mathrm{GSp}(2n, \mathbb{F}_q)$ and $\mathrm{GO}^{\pm}(2n, \mathbb{F}_q)$ denote the symplectic and orthogonal groups of similitudes…

The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of generators. For a finite solvable group $G$ of order $N = p_{1}p_{2}\dots p_{n}$, where $p_{i}$'s are…

We apply the ideas of derived algebraic geometry and topological field theory to the representation theory of reductive groups. Our focus is the Hecke category of Borel-equivariant D-modules on the flag variety of a complex reductive group…

Let $\mathbb{F}$ be an algebraically closed field and $G$ be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups $H<G$ and $\mathbb{F} G$-modules $L$ such that the restriction…

In this paper, I introduce weak representations of a Lie groupoid $G$. I also show that there is an equivalence of categories between the categories of 2-term representations up to homotopy and weak representations of $G$. Furthermore, I…

We investigate the distribution of the angles of Gauss sums attached to the cuspidal representations of general linear groups over finite fields. In particular we show that they happen to be equidistributed w.r.t.the Haar measure. However,…

Let G be a subgroup of GL(V), where V is a finite dimensional vector space over a finite field of characteristic p >0. If det(g-1) = 0 for all g \in G then we call G a fixed-point subgroup of GL(V). Motivated in parallel by questions in…

We study the category $\textrm{Rep}(Q,\mathbb{F}_1)$ of representations of a quiver $Q$ over "the field with one element", denoted by $\mathbb{F}_1$, and the Hall algebra of $\textrm{Rep}(Q,\mathbb{F}_1)$. Representations of $Q$ over…

We prove that any smooth irreducible supersingular representation with central character of $\text{GL}_2(F)$ is never of finite presentation when $F$ is a finite field extension of $\mathbb{Q}_p$ such that $F\neq \mathbb{Q}_p$, extending a…

Assume $\mathbf{G}$ is a connected reductive algebraic group defined over an algebraic closure $\mathbb{K} = \overline{\mathbb{F}}_p$ of the finite field of prime order $p>0$. Furthermore, assume that $F : \mathbf{G} \to \mathbf{G}$ is a…

We classify Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of 0704.0195v2 this gives a complete description of all braided tensor equivalent pairs of twisted quantum…