Related papers: Characters of some simple supercuspidal representa…

Let $F$ be a non-archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. To construct types for supercuspidal representations of $G$, simple types by S\'echerre and Yu's construction are…

We establish an explicit formula for twisted Harish-Chandra characters of toral supercuspidal representations of p-adic reductive groups under several technical assumptions. Our setup especially includes the case of a quasi-split group…

We obtain an upper bound for the dimension of the cuspidal automorphic forms for $\mathrm{GL}_2$ over a number field, whose archimedean local representations are not tempered. More precisely, we prove the following result. Let $F$ be a…

Let E/F be a quadratic extension of number fields. For a cuspidal representation $\pi$ of SL(2,A_E), we study the non-vanishing of the period integral on SL(2,F)\SL(2,A_F). We characterise the non-vanishing of the period integral of $\pi$…

For semisimple Lie superalgebras over an algebraically closed field of characteristic zero, whose category of finite dimensional super representations is semisismple, we classify all irreducible super representations for which the…

This paper completes description of categories of representations of finite-dimensional simple unital Jordan superalgebras over algebraically closed field of characteristic zero.

Let $F$ be a non-archimedean local field. We show that any representation of a maximal compact subgroup of $\mathbf{SL}_N(F)$ which is typical for an essentially tame supercuspidal representation must be induced from a Bushnell--Kutzko…

Let $G$ be the group of rational points of a general linear group over a non-archimedean local field $F$. We show that certain representations of open, compact-mod-centre subgroups of $G$, (the maximal simple types of Bushnell and Kutzko)…

Let F be a locally compact non-archimedean field, p its residue characteristic, and G a connected reductive group over F. Let C an algebraically closed field of characteristic p. We give a complete classification of irreducible admissible…

Let $F$ be a non-archimedean local field with odd residual characteristic, and let $H$ be a maximal torus of ${\rm GL}_2(F)$. In this paper, we will classify the irreducible $H$-distinguished representations of ${\rm GL}_2(F)$ by using…

Let $G$ denote the unramified quasi-split unitary group $\mathbb{U}(1,1)(F)$ over a $p$-adic field $F$ with residual characteristic $p \neq 2$. In this article, we determine the branching rules for all irreducible supercuspidal…

Let p be an arbitrary prime number and k be an algebraically closed field of characteristic l different from p. We construct maximal simple k-types of Levi subgroups M' of SLn(F), when F is a non-archimedean locally compact field of…

Let $F$ be a finite field, and let $\mathbb{E}$ be either a quadratic field extension $E/F$ or the split algebra $F \oplus F$. We study distinguished representations of $\rm{SL}_{2n}(F)$ by the subgroup $H_{\flat} := \rm{SL}_{2n}(F) \cap…

We give a motivic proof of a character formula for depth zero supercuspidal representations of $p$-adic SL(2). We begin by finding the virtual Chow motives for the character values of all depth zero supercuspidal representations of $p$-adic…

We study the local Langlands functoriality transfer from $\text{SO}(5, F)$ to $\text{GL}(4, F)$ for arbitrary twists of several families of irreducible supercuspidal representations of $\text{GL}(4, F)$, where $F$ is a non-archimedean local…

Suppose that $\mathbf{G}$ is a connected reductive group over a finite extension $F/\mathbb{Q}_p$, and that $C$ is a field of characteristic $p$. We prove that the group $\mathbf{G}(F)$ admits an irreducible admissible supercuspidal, or…

We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.

In 2014, Reeder and Yu constructed epipelagic representations of a reductive $p$-adic group $G$ from stable functions on shallowest Moy-Prasad quotients. In this paper, we extend these methods when $G$ is split. In particular, we classify…

Arthur classified the discrete automorphic representations of symplectic and orthogonal groups over a number field by that of the general linear groups. In this classification, those that are not from endoscopic lifting correspond to pairs…

Let $F$ be a non-archimedean local field of odd residual characteristic. We compute the Jordan set of a simple cuspidal representation of a symplectic group over $F$, using explicit computations of generators of the Hecke algebras of covers…