Related papers: Globally analytic principal series representation …

We study the Steinberg lattice of the general linear group when reduced modulo a prime different from the defining characteristic.

By applying the formula for essential Whittaker functions established by Matringe and Miyauchi, we study five integral representations for irreducible admissible generic representations of ${\rm GL}_n$ over $p$-adic fields. In each case, we…

Any finite-dimensional $p$-adic representation of the absolute Galois group of a $p$-adic local field with imperfect residue field is characterized by its arithmetic and geometric Sen operators defined by Sen and Brinon. We generalize their…

The object of this article is to study some aspects of the quantum geometric Langlands program in the language of vertex algebras. We investigate the representation theory of the vertex algebra of chiral differential operators on a…

In this paper we prove the forward direction of the conjecture of Gross-Prasad that an L-packet $\Pi_\phi(G)$ contains a generic representation if and only if $L(s, \phi, \Ad)$ is regular at $s=1$, by assuming the local Langlands…

Fix an odd prime $p$. Let $G$ be a compact $p$-adic Lie group containing a closed, normal, pro-$p$ subgroup $H$ which is abelian and such that $G/H$ is isomorphic to the additive group of $p$-adic integers $\mathbbZ_p$ . First we assume…

Recently, Iwahori-Hecke algebras were associated to Kac-Moody groups over non-Archimedean local fields. We introduce principal series representations for these algebras. We study these representations and partially generalize Kato and…

Let $\Lambda$ be a lattice in a second countable, locally compact abelian group $G$ with annihilator $\Lambda^{\perp} \subseteq \widehat{G}$. We investigate the validity of the following statement: For every $\eta$ in the Feichtinger…

Let $\Pi$ be a cuspidal automorphic representation of $\mathrm{GL}_{2n}(\mathbb{A_Q})$ and let $p$ be an odd prime at which $\Pi$ is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded $p$-adic…

We show that the cyclotomic Iwasawa--Greenberg Main Conjecture holds for a large class of modular forms with multiplicative reduction at $p$, extending previous results for the good ordinary case. In fact, the multiplicative case is deduced…

We study the structure of minimal parabolic subgroups of the classical infinite dimensional real simple Lie groups, corresponding to the classical simple direct limit Lie algebras. This depends on the recently developed structure of…

We provide a family of representations of GL(2n) over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(2n)- distinguished). While our result generalizes a…

We propose a p-adic Langlands correspondence in families.

Let $F$ be a finite extension of $\mathbb{Q}_p$. The so-called supersingular representations are the basic building blocks in the theory of mod $p$ representations of ${\rm GL}_2(F)$. The space of pro-$p$-Iwahori invariants of a universal…

Let $p$ be an odd prime and $L/K$ a $p$-adic Lie extension whose Galois group is of the form $\mathbb{Z}_p^{d-1}\rtimes \mathbb{Z}_p$. Under certain assumptions on the ramification of $p$ and the structure of an Iwasawa module associated to…

We prove that Novodvorsky's definition of local L-factors for generic representations of GSp(4) x GL(2) is compatible with the local Langlands correspondence when the GL(2) representation is non-supercuspidal. We also give an interpretation…

The evaluation homomorphisms from the Yangian Y(gl_n) to the universal enveloping algebra U(gl_n) allow one to regard the irreducible finite-dimensional representations of gl_n as Yangian modules. We give necessary and sufficient conditions…

Let $K$ be a finite unramified extension of $\mathbb{Q}_p$ with $p > 3$. We study the extremely non--generic irreducible components in the reduced part of the Emerton--Gee stack for $\mathrm{GL}_2$. We show precisely which irreducible…

This paper focuses on the $GL_n$ tensor product algebra, which encapsulates the decomposition of tensor products of arbitrary finite dimensional irreducible representations of $GL_n$. We will describe an explicit basis for this algebra.…

We combine the geometric realization of principal series representations of the author, with the Bott--Borel--Weil Theorem for direct limits of compact groups of Natarajan, Rodriguez-Carrington and the author, obtaining limits of principal…