Related papers: Weil representations and metaplectic groups over a…

We show that the irreducible representation of the asymptotic Hecke algebra corresponding to a special representation of a Weyl group admits a basis with strong positivity properties.

The irreducible representations $\phi_n^1$ and $\phi_n^2$ of the symplectic group $G_n=Sp_{2n}(P)$ over an algebraically closednfield $P$ of characteristic $p>2$ with highest weights $\omega_{n-1}+\frac{p-3}{2}\omega_n$ and…

We describe the structure of the Whittaker or Gelfand-Graev module on a $n$-fold metaplectic cover of a $p$-adic group $G$ at both the Iwahori and spherical level. We express our answer in terms of the representation theory of a quantum…

Let F be a local field of positive characteristic, and let G be either a Heisenberg group over F, or a certain (nonabelian) two-dimensional unipotent group over F. If H is an arithmetic subgroup of G, we provide an explicit description of…

Let $K$ be an arbitrary field of characteristic zero and $A$ a commutative associative $ K$-algebra which is an integral domain. Denote by $R$ the fraction field of $A$ and by $W(A)=RDer_{\mathbb K}A,$ the Lie algebra of $\mathbb…

Let $k$ be an algebraically closed field of characteristic $l\neq p$. We construct maximal simple cuspidal $k$-types of Levi subgroups $\mathrm{M}'$ of $\mathrm{SL}_n(F)$, when $F$ is a non-archimedean locally compact field of residual…

Let $F$ be a non-archimedean locally compact field of residual characteristic $p$, let $G=\mathrm{GL}_{r}(F)$ and let $\widetilde{G}$ be an $n$-fold metaplectic cover of $G$ with $\mathrm{gcd}(n,p)=1$. We study the category…

Let F be a non-Archimedean local field of residue characteristic p. In this paper, we first compute the reduction modulo p of irreducible smooth representations of a quaternion division algebra over F and of two-dimensional irreducible…

Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we…

Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…

We construct and study the holomorphic discrete series representation and the principal series representation of the symplectic group $\mathrm{Sp}(2n,F)$ over a $p$-adic field $F$ as well as a duality between some sub-representations of…

Let $F$ be a non-Archimedean local field with odd characteristic $p$. Let $N$ be a positive integer and $G=Sp_{2N}(F)$. By work of Lomel\'i on $\gamma$-factors of pairs and converse theorems, a generic supercuspidal representation $\pi$ of…

In this third paper in a series on type I Howe duality for finite fields, we give a complete description of the restriction of the oscillator representation over a finite field to products of dual pairs of symplectic and orthogonal groups…

Using exceptional theta correspondences, we prove that certain Weil representations of $p$-adic groups are multiplicity free and determine irreducible quotients.

Let $F$ be a nonarchimedean local field of characteristic zero and let SL(N) = SL(N,F). This article is devoted to studying the influence of the elliptic representations of SL(N) on the $K$-theory. We provide full arithmetic details. This…

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…

Let F be a local field. The action of GL(n,F) on the Grassmann variety Gr(m,n,F) induces a continuous representation of the maximal compact subgroup of GL(n,F) on the space of L^2-functions on Gr(m,n,F). The irreducible constituents of this…

One of the most beautiful results in the integral representation theory of finite groups is a theorem of A. Weiss that detects a permutation $R$-lattice for the finite $p$-group $G$ in terms of the restriction to a normal subgroup $N$ and…

Let $G$ be a connected reductive group over a finite field $\mathfrak{f}$ of order $q$. When $q$ is small, we make further assumptions on $G$. Then we determine precisely when $G(\mathfrak{f})$ admits irreducible, cuspidal representations…

This paper is a significant part of a general project aimed to classify all irreducible representations of finite quasi-simple groups over an algebraically closed field, in which the image of at least one element is represented by an almost…