Related papers: Supercuspidal representations: construction, class…

Pseudo $H$-type Lie algebras are a special class of 2-step nilpotent metric Lie algebras, intimately related to Clifford algebras $\Cl_{r,s}$. In this work we propose the classification method for integral orthonormal structures of pseudo…

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

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…

It is generally believed (and for the most part is probably true) that Lie theory, in contrast to the characteristic zero case, is insufficient to tackle the representation theory of algebraic groups over prime characteristic fields.…

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations…

Let $\mathbf{G}$ be an unramified quasi-split unitary group over a p-adic field of odd residual characteristic. The goal of this paper is to describe the supercuspidal representations within certain L-packets of $\mathbf{G}$, which are…

We give an explanation of the bijection between geometric and arithmetic diagrams attached to supercuspidal unipotent representations of a simple p-adic group which is based purely on algebra. The second version contains much additional…

We construct a Langlands parameterization of supercuspidal representations of $G_2$ over a $p$-adic field. More precisely, for any finite extension $K / \QQ_p$ we will construct a bijection \[ \CL_g : \CA^0_g(G_2,K) \rightarrow \CG^0(G_2,K)…

Let G be a connected split adjoint semi simple p-adic Lie group. This paper can be seen as a continuation of [12] and is about the construction of locally analytic G-representations which do not lie in the principal series. Here we consider…

Let $\rm E/\rm F$ be an unramified quadratic extension of local non archimedean fields of characteristic 0. Let $\underline{H}$ be an algebraic reductive group, defined and split over $\rm F$. We assume that the split connected component of…

We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…

In this paper, we use type theory to construct a family of depth $\frac{1}{N}$ minimax supercuspidal representations of $\text{GL}(2N, F)$ which we call middle supercuspidal representations. These supercuspidals may be viewed as a natural…

This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…

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.…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…

This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…

In this paper we describe the new model of the representations of the current groups with a semisimple Lie group of the rank one. In the earlier papers of 70-80-th (Araki, Gelfand-Graev-Vershik) had posed the problem about irreducible…

Let $X$ be a smooth and proper scheme over an algebraically closed field. The purpose of the current text is twofold. First, we construct the moduli stack parametrizing rank $n$ continuous $p$-adic representations of the \'etale fundamental…

In this paper we explore some properties of H-structures. We describe a construction of H-structures based on one-dimensional asymptotic classes which preserves pseudo-finiteness. That is, the H-structures we construct are ultraproducts of…

In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the…