Related papers: Complements on disconnected reductive groups
Let $\mathbb{F}_{q}$ be a finite field of characteristic $p$, and let $W_{2}(\mathbb{F}_{q})$ be the ring of Witt vectors of length two over $\mathbb{F}_{q}$. We prove that for any reductive group scheme $\mathbb{G}$ over $\mathbb{Z}$ such…
The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.
The goal of these notes is to give a self-contained account of the representation theory of $GL_2$ and $SL_2$ over a finite field, and to give some indication of how the theory works for $GL_n$ over a finite field.
In this paper we provide a geometric framework for the study of characters of depth-zero representations of unramified groups over local fields with finite residue fields which is built directly on Lusztig's theory of character sheaves for…
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.
Let $k$ be a field of characteristic $0$. We consider principal bundles over a $k$-scheme with reductive structure group (not necessarily of finite type). It is showm in particular that for $k$ algebraically closed there exists on any…
We address the problem of finding necessary and sufficient conditions for an arbitrary group, not necessarily finite, to admit a faithful irreducible representation over an arbitrary field.
This paper surveys basic properties of finite presentation in groups, Lie algebras and rings. It includes some new results and also new, more elementary proofs, of some results that are already in the literature. In particular, we discuss…
We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give…
This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…
We construct the local Langlands correspondence of essentially unipotent supercuspidal representations under the framework of rigid inner forms and prove a certaion functoriality and compatibilities. This result is stronger than the…
We generalize the methods of Moy-Prasad, in order to define and study the genuine depth zero representations of some nonlinear covers of reductive groups over $p$-adic local fields. In particular, we construct all depth zero supercuspidal…
We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…
In the paper we study irreducible representations of some nilpotent groups of finite abelian total rank. The main result of the paper states that if a torsion-free minimax group $G$ of nilpotency class 2 admits a faithful irreducible…
Let $G$ be a simple algebraic group defined over a finite field of good characteristic, with associated Frobenius endomorphism $F$. In this article we extend an observation of Lusztig, (which gives a numerical relationship between an…
In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.
We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.
How does an irreducible representation of a group behave when restricted to a subgroup? This is part of branching problems, which are one of the fundamental problems in representation theory, and also interact naturally with other fields of…
This survey article has two components. The first part gives a gentle introduction to Serre's notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second…
In this note we give a complete classification of all indecomposable yet reducible representations of $B_3$ for dimensions $2$ and $3$ over an algebraically closed field $K$ with characteristic $0$, up to equivalence. We illustrate their…