Related papers: Affine Springer fibers and depth zero L-packets

Let $\Pi$ be a cohomological cuspidal automorphic representation of ${\rm GL}_{2n}(\mathbb A)$ over a totally real number field $F$. Suppose that $\Pi$ has a Shalika model. We define a rational structure on the Shalika model of $\Pi_f$.…

In this paper, we study an algebraic fiber space in positive characteristic whose generic fiber $F$ has finitely generated canonical ring and sufficiently large Frobenius stable canonical ring. An example of such a case is when $F$ is…

For a locally compact, totally disconnected group $G$, a subgroup $H$ and a character $\chi:H \to \mathbb{C}^{\times}$ we define a Hecke algebra $\mathcal{H}_\chi$ and explore the connection between commutativity of $\mathcal{H}_\chi$ and…

We show that for any tame regular discrete series parameter of GSp_4 or its inner form GU_2(D), the L-packet attached by the local Langlands conjecture agrees with the L-packet of depth zero supercuspidal representations constructed by…

Let $F$ be a non-archimedean locally compact field of residue characteristic $p\neq2$, let $G=\mathrm{GL}_{n}(F)$ and let $H$ be an orthogonal subgroup of $G$. For $\pi$ a complex smooth supercuspidal representation of $G$, we give a full…

Let F be a finite extension of Q_p and let G be a connected reductive group over F. We assume that p is big relatively to G. Let G' be an endoscopic group of G. Following Arthur, we have, roughly speaking, a spectral transfer which, to a…

Let $G$ be a $\mathbb{Q}_p$-split reductive group with connected centre and Borel subgroup $B=TN$. We construct a right exact functor $D^\vee_\Delta$ from the category of smooth modulo $p^n$ representations of $B$ to the category of…

We construct a bijection between admissible representations for an affine Lie algebra $\mathfrak{g}$ at boundary admissible levels and $\mathbb{C}^\times$ fixed points in homogeneous elliptic affine Springer fibres for the Langlands dual…

In this paper, we prove Lusztig's conjecture for finite special linear groups, i.e., we show that characteristic functions of character sheaves coincide with almost characters up to scalar constants, under the condition that the…

If $\pi$ is a representation of a $p$-adic group $G(F)$, and $\phi$ is its Langlands parameter, can we use the moduli space of Langlands parameters to find a geometric property of $\phi$ that will detect when $\pi$ is generic? In this paper…

Let $G$ be a simply connected semisimple algebraic group over $\mathbb{C}$ and let $\rho :G\rightarrow GL(V_\lambda)$ be an irreducible representation of highest weight $\lambda$. Suppose that $\rho$ has finite kernel. Springer defined…

This is the first of two articles aiming to introduce symplectic spinors into the field of symplectic topology and the subject of Frobenius structures. After exhibiting a (tentative) axiomating setting for Frobenius structures resp. 'Higgs…

In previews works, joint with N. Gurevitch, a family of Rankin-Selberg integrals were shown to represent the twisted standard $\mathcal{L}$-function $\mathcal{L}\left(s,\pi,\chi,\mathfrak{st}\right)$ of a cuspidal representation $ \pi$ of…

We construct a pinning-normalized local Langlands correspondence for depth-zero supercuspidal representations of a connected reductive group over a non-archimedean local field. After fixing a pinned splitting of the quasi-split inner form,…

Let $G$ be a reductive group over a number field $F$, which is split at a finite place $\mathfrak{p}$ of $F$, and let $\pi$ be a cuspidal automorphic representation of $G$, which is cohomological with respect to the trivial coefficient…

The main goal of this note is to show that the local L-packet of Fargues-Scholze [FS], corresponding to an elliptic L-parameter, has an endoscopic decomposition. Our argument is strongly motivated by a beautiful paper of Chenji Fu [Fu],…

Let ${\bf G}$ be a simply connected semisimple algebraic group over $\Bbbk=\bar{\mathbb{F}}_q$, the algebraically closure of $\mathbb{F}_q$ (the finite field with $q=p^e$ elements), and $F$ be the standard Frobenius map. Let ${\bf B}$ be an…

Let $F$ be a local non archimedian field of characteristic $0$, and $G$ a non-connected reductive group over $F$. We denote $G^0$ the connected component of the identity and assume the quotient $G/G^0$ is abelian. For $f$ a locally constant…

We introduce a new invariant of Borel reducibility, namely the notion of thickness; this associates to every sentence $\Phi$ of $\mathcal{L}_{\omega_1 \omega}$ and to every cardinal $\lambda$, the thickness $\tau(\Phi, \lambda)$ of $\Phi$…

A result of Lehrer describes a beautiful relationship between topological and combinatorial data on certain families of varieties with actions of finite reflection groups. His formula relates the cohomology of complex varieties to point…