Related papers: Arithmetic Branching Law and generic $L$-packets

We show how the modular representation theory of inner forms of general linear groups over a non-Archimedean local field can be brought to bear on the complex theory in a remarkable way. Let F be a non-Archimedean locally compact field of…

We prove a prime number theorem first for the classical Rankin-Selberg L-function $L(s,\pi\times\pi')$ over any Galois extension with $\pi$ and $\pi'$ unitary automorphic cuspidal representations of $GL_n$ and $GL_m$ respectively with at…

Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $\pi$ an irreducible admissible representation of $G$. In this article we prove a necessary and sufficient condition for the finiteness of the multiplicities of $L$-types…

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

Let $G/H$ be a reductive symmetric space over a $p$-adic field $F$, the algebraic groups $G$ and $H$ being assumed semisimple of relative rank $1$. One of the branching problems for the Steinberg representation $\St_G$ of $G$ is the…

We give a complete description of the discrete spectra in the branching law $\Pi|_{G'}$ with respect to the pair $(G,G')=(O(p,q), O(p',q') \times O(p'',q''))$ for irreducible unitary representations $\Pi$ of $G$ that are "geometric…

We prove a quantitative local limit theorem for the number of descents in a random permutation. Our proof uses a conditioning argument and is based on bounding the characteristic function $\phi(t)$ of the number of descents. We also…

Let $F$ be a non-archimedean local field and $G={\bf{G}}(F)$ the group of $F$-rational points of a connected reductive $F$-group. Then we have the Langlands classification of complex irreducible admissible representations $\pi$ of $G$ in…

In \cite{JZ1}, D. Jiang and L. Zhang proposed a conjecture which related the wavefront sets and the descent method in the local fields case. Recently, in \cite{JLZ}, they and D. Liu define the arithmetic wavefront set of certain irreducible…

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. To any irreducible smooth…

Let $F$ be a non-Archimedean local field. This paper studies homological properties of irreducible smooth representations restricted from $\mathrm{GL}_{n+1}(F)$ to $\mathrm{GL}_n(F)$. A main result shows that each Bernstein component of an…

We wish to understand how irreducible representations of a group G behave when restricted to a subgroup G' (the branching problem). Our primary concern is with representations of reductive Lie groups, which involve both algebraic and…

Let $F$ be a non-archimedean local field of residue characteristic $p$, $G$ be the group $GL(n, F)$. In this note, under the assumption $(n, p)=1$, we show a simple cuspidal representation $\pi$ (that with normalized level $\frac{1}{n}$) of…

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…

In this paper we consider the restriction of a unitary irreducible representation of type $A_{\mathfrak q}(\lambda)$ of $GL(4,{\mathbb R})$ to reductive subgroups $H$ which are the fixpoint sets of an involution. We obtain a formula for the…

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 $\pi_1$ be a standard representation of $\mathrm{GL}_{n+1}(F)$ and let $\pi_2$ be the smooth dual of a standard representation of $\mathrm{GL}_n(F)$. When $F$ is non-Archimedean, we prove that $\mathrm{Ext}^i_{\mathrm{GL}_n(F)}(\pi_1,…

Let $\Pi$ be an irreducible unitary completion of a locally algebraic ${\rm GL}_2(\qp)$-representation. We describe those first-order deformations of $\Pi$ which are themselves completions of a locally algebraic representation. This answers…

A cuspidal automorphic representation \pi of a group G is said to to be distinguished with respect to a subgroup H if the integral of f along H is nonzero for a cusp form f in the space of \pi. Such period integrals are related to…

Let $F$ be a non Archimedean local field with odd residual characteristic, and let $K$ be a hyperspecial maximal compact subgroup of the $p$-adic symplectic group $G=\mathrm{Sp}_4(F)$. Let $\mathfrak{s}$ be an inertial class for $G$ in the…