Related papers: On typical representations for depth-zero componen…

Let $K := \mathrm{GL}_n(\mathcal{O})$ denote the maximal compact subgroup of $\mathrm{GL}_n(F)$, where $F$ is a nonarchimedean local field with ring of integers $\mathcal{O}$. We study the decomposition of the space of locally constant…

We give the decomposition into irreducible representations of the restriction to a maximal compact subgroup of any irreducible depth-zero supercuspidal representation of $\mathrm{SL}(2,F)$ when $F$ is a local nonarchimedean field of…

Let $G$ be an exceptional simple algebraic group over an algebraically closed field $k$ and suppose that the characteristic $p$ of $k$ is a good prime for $G$. In this paper we classify the maximal Lie subalgebras $\mathfrak{m}$ of the Lie…

Let $G$ be a split reductive group over a local field $\bK$, and let $G((t))$ be the corresponding loop group. In \cite{GK} we have introduced the notion of a representation of (the group of $\bK$-points) of $G((t))$ on a pro-vector space.…

Let $\mathbf{G}$ be a connected reductive complex algebraic group with split real form $(G,\sigma)$. Consider a strict wonderful $\mathbf{G}$-variety $\bf{X}$ equipped with its $\sigma$-equivariant real structure, and let $X$ be the…

We prove that, for every modulus $\mathfrak{q}$, every class of the narrow ray class group $H_{\mathfrak{q}}(\mathbf{K})$ of an arbitrary number field $\mathbf{K}$ contains a product of three unramified prime ideals $\mathfrak{p}$ of degree…

Let n be a positive integer, F be a non-Archimedean locally compact field of odd residue characteristic p and G be an inner form of GL(2n,F). This is a group of the form GL(r,D) for a positive integer r and division F-algebra D of reduced…

Let $\mathbf{G}(\mathsf{k})$ be a semisimple $p$-adic group, inner to split. In this article, we compute the algebraic and canonical unramified wavefront sets of the irreducible supercuspidal representations of $\mathbf{G}(\mathsf{k})$ in…

Let $\pi $ be an irreducible smooth complex representation of a general linear $p$-adic group and let $\sigma $ be an irreducible complex supercuspidal representation of a classical $p$-adic group of a given type, so that $\pi\otimes\sigma…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

Let $K$ be an imaginary quadratic field different from $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-3})$. For a positive integer $N$, let $K_\mathfrak{n}$ be the ray class field of $K$ modulo $\mathfrak{n}=N\mathcal{O}_K$. By using the…

We study the role of the mirabolic subgroup $P$ of $G=\mathbf{GL}_n(F)$ ($F$ a $p$-adic field) in smooth irreducible representations of $G$ that possess a non-zero invariant functional relative to a subgroup of the form $H_{k} =…

Let $p$ be a prime, and $F$ a non-archimedean local field with residue characteristic $p$ and ring of integers $\mathcal{O}_{F}$. Set $G_{S}:={\rm SL}_{2}(F)$and $K_{0}:={\rm SL}_{2}(\mathcal{O}_{F})$ . For a smooth irreducible…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

Let $F$ be a local field with residue characteristic $p$, let $C$ be an algebraically closed field of characteristic $p$, and let $\mathbf{G}$ be a connected reductive $F$-group. In a previous paper, Florian Herzig and the authors…

The general linear group GL(n, K) over a field K contains a particularly prominent subgroup U(n, K), consisting of all the upper triangular unipotent elements. In this paper we are interested in the case when K is the finite field F_q, and…

This paper provides results on the modular representation theory of the supergroup $GL(m|n).$ Working over a field of arbitrary characteristic, we prove that the explicit combinatorics of certain crystal graphs describe the representation…

Let $F$ be a non-Archimedean locally compact field of residual characteristic $p$ with $p\neq 2$. Let $n$ be a power of $p$ and let $G$ be an inner form of the general linear group $\text{\rm GL}_n(F)$. We give a transparent parametrization…

We define eventually symmetric functions to be those power series of bounded degree in infinitely many variables that are invariant under interchanging all the variables with large enough indices. We show how this ring $\tilde{\Lambda}$ is…

Let F be a local field with finite residue field of characteristic p and k an algebraic closure of the residue field. Let G be the group of F-points of a F-split connected reductive group. In the apartment corresponding to a chosen maximal…