Related papers: Repr\'esentations supercuspidales

A method to construct irreducible unitary representations of a hyperspecial compact subgroup of a reductive group over p-adic field with odd p is presented. Our method is based upon Cliffods theory and Weil representations over finite…

A paper of Reeder-Yu gives a construction of epipelagic supercuspidal representations of $p$-adic groups. The input for this construction is a pair $(\lambda, \chi)$ where $\lambda$ is a stable vector in a certain representation coming from…

We describe a special case of base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both defined over a p-adic field of odd residual characteristic. Roughly speaking, we require the…

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…

We give combinatorial models for complex, smooth, non-spherical, generic, irreducible representations of the group G=PGL(2,F), where F is a non-archimedean locally compact field. They use the graphs X_k lying above the tree of G, introduced…

Let K be a non-archimedean local field and let G be a connected reductive K-group which splits over an unramified extension of K. We investigate supercuspidal unipotent representations of the group G(K). We establish a bijection between the…

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…

Representations of four dimensional superconformal groups are constructed as fields on many different superspaces, including super Minkowski space, chiral superspace, harmonic superspace and analytic superspace. Any unitary irreducible…

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…

This paper develops the theory of distinguished regular supercuspidal representations, and it highlights how the correspondence between regular characters and regular supercuspidal representations resembles induction in certain ways.

We construct tame types for connected reductive p-adic groups. We also discuss their exhaustion and equivalence.

Reeder and Yu have recently given a new construction of a class of supercuspidal representations called epipelagic representations. We explicitly calculate the Local Langlands Correspondence for certain families of epipelagic…

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 F be a non Archimedean locally compact field and let D be a central F-division algebra. We prove that any positive level supercuspidal irreducible representation of the group GL(m,D) is compactly induced from a representation of a…

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…

The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this…

In this paper we study quantitative aspects of trace characters $\Theta_\pi$ of reductive $p$-adic groups when the representation $\pi$ varies. Our approach is based on the local constancy of characters and we survey some other related…

Given a $p$-adic group $G=\mathbf{G}(F)$ and a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$ such that the fixed-point subgroup $\mathbf{G}^\Gamma$ is reductive, we show that every semisimple character (in the sense of Bushnell and…

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the…

We give a modification of Yu's construction of supercuspidal representations of a connected reductive group over a non-archimedean local field. This modification restores the validity of certain key intertwining property claims made by Yu,…