Related papers: Complements on disconnected reductive groups
In this article, we classify disconnected reductive groups over an algebraically closed field with a few caveats. Internal parts of our result are both a classification of finite groups and a classification of integral representations of a…
We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual…
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…
We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.
This is a preliminary version of the first chapter of a book project on the character theory of finite groups of Lie type. It provides the foundations from the general theory of reductive algebraic groups over a finite field.
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
We present a selection of results contributing to a structure theory of totally disconnected locally compact groups.
We relate a generic character sheaf on a disconnected reductive group with a character of a representation of the rational points of the group over a finite field extending a result known in the connected case.
We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.
We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.
In this paper, we describe the possible disconnected complex reductive algebraic groups $E$ with component group $\Gamma = E/E_0$. We show that there is a natural bijection between such groups $E$ and algebraic extensions of $\Gamma$ by…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.
We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.
We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…
This work completes the classification of the imprimitive irreducible modules, over algebraically closed fields of characteristic 0, of the finite quasisimple groups.
These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed…
We study the completion of a group relative to a Zariski dense representation in a reductive algebraic group over a field $k$. The characteristic zero case was worked out previously by R. Hain; we extend his results to arbitrary…
This paper reviews recent results and open problems on the conductor of finite group characters, highlighting their connections to one another and to broader topics in the representation theory of finite groups.
Let $k$ be a nonperfect separably closed field. Let $G$ be a (possibly non-connected) reductive group defined over $k$. We study rationality problems for Serre's notion of complete reducibility of subgroups of $G$. In our previous work, we…