Related papers: Disconnected Reductive Groups: Classification and …
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…
This paper proves the existence of cuspidal automorphic forms for a reductive group, invariant under an automorphism of finite order. The techniques used are a local analysis of orbital integrals and the Arthur-Selberg trace formula.
This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…
A finite group G is said to be a cut group if all central units in the integral group ring ZG are trivial. In this article, we extend the notion of cut groups, by introducing extended cut groups. We study the properties of extended cut…
We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…
This work completes the classification of the imprimitive irreducible modules, over algebraically closed fields of characteristic 0, of the finite quasisimple groups.
The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence…
We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
We prove the following result related to the inverse problem for universal deformation rings of group representations: Given a finite field k, denote by W(k) the ring of Witt vectors over k and by K the field of fractions of W(k). If a…
We introduce and develop a categorification of the theory of Real representations of finite groups. In particular, we generalize the categorical character theory of Ganter--Kapranov and Bartlett to the Real setting. Given a Real…
We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their…
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…
Among connected linear algebraic groups, quasi-reductive groups generalize pseudo-reductive groups, which in turn form a useful relaxation of the notion of reductivity. We study quasi-reductive groups over non-archimedean local fields,…
We show that the class of inductive limits of the representations of finite symmetric groups with simple spectrum coinsides with the class of Markov representations of the infinite symmetric group associated with Markov measures on the…
A new proof of the classification for tensor ideal thick subcategories of the bounded derived category, and the stable category, of modular representations of a finite group is obtained. The arguments apply more generally to yield a…
In this short note we show that every connected reductive simply-connected algebraic group of rank $>1$ over the complex numbers has infinitely many pairs of irreducible representations which are not related by an automorphism of the…
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
In the monograph arXiv:2108.03453, we define the notion of a unipotent representation of a complex reductive group. The representations we define include, as a proper subset, all special unipotent representations in the sense of…
We develop a functorial theory of spinor and oscillator representations parallel to the theory of Schur functors for general linear groups. This continues our work on developing orthogonal and symplectic analogues of Schur functors. As…