Related papers: Exceptional supercuspidal representations in small…

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…

Let F be a nonarchimedean local field whose residue field has at least four elements. Let G be a connected reductive group over F that splits over a tamely ramified field extension of F. We provide a construction of supercuspidal…

We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu's construction from data satisfying a certain compactness condition. Each character is…

We show that a mod-$\ell$-representation of a p-adic group arising from the analogue of Yu's construction is supercuspidal if and only if it arises from a supercuspidal representation of a finite reductive group. This has been previously…

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these…

Let F be a non-archimedean local field of odd residual characteristic. Let G be a (connected) reductive group over F that splits over a tamely ramified field extension of F. We revisit Yu's construction of smooth complex representations of…

Let F be a non-archimedean local field of odd residual characteristic p. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu's construction of complex…

This text is a response to the following question: What are the methods to build supercuspidal complex representations of p-adic reductive groups and are there ties between them ? We will give an overview of the Bushnell-Kutzko and Yu…

A new approach to Jiu-Kang Yu's construction of tame supercuspidal representations of $p$-adic reductive groups is presented. Connections with the theory of cuspidal Deligne-Lusztig representations of finite groups of Lie type are also…

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…

Let $G$ be a reductive $p$-adic group. We prove that all supercuspidal representations of $G$ arise through Yu's construction subject to certain hypotheses on $k$ (depending on $G$). As a corollary, under the same hypotheses, we see that…

Let $G$ be a p-adic classical group (orthogonal, symplectic, unitary) and $\pi$ be an epipelagic representation of $G$ defined by Reeder-Yu. Using M{\oe}glin's theory of extended cuspidal supports and Bushnell-Kutzko's theory of covering…

The group $\GL_2$ over a local field with (residue) characteristic $2$ possesses much more smooth supercuspidal $\ell$-adic representations, than over a local field of residue characteristic $> 2$. One way to construct these representations…

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 $F$ be a non-archimedean local field of residual characteristic $p$. Let $\mathbb{G}$ be a reductive group defined over $F$ which splits over a tamely ramified extension and set $G=\mathbb{G}(F)$. We assume that $p$ does not divide the…

The author's work with Murnaghan on distinguished tame supercuspidal representations is re-examined using a simplified treatment of Jiu-Kang Yu's construction of tame supercuspidal representations of $p$-adic reductive groups. This leads to…

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…

This paper studies the behavior of Jiu-Kang Yu's tame supercuspidal representations relative to involutions of reductive p-adic groups. Symmetric space methods are used to illuminate various aspects of Yu's construction. Necessary…

We compare precisely and explicitly Bushnell-Kutzko and Yu's constructions of supercuspidal representations. At the end, we draw conclusions and ask a natural question about the existence of a general construction.

This paper simplifies and further develops various aspects of Tasho Kaletha's construction of regular supercuspidal representations. Moreover, Kaletha's construction is connected with the author's revision of Yu's construction of tame…