相关论文: Whittaker-Shintani functions for Fourier-Jacobi mo…

We show that the explicit formula of Stanley-F\'eray-\'Sniady for the characters of the symmetric group have a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel'fand pair $(S_n\times…

We formulate an analogue of the Ichino-Ikeda conjectures for the Whittaker-Fourier coefficients of automorphic forms on quasi-split reductive groups. This sharpens the conjectures of Sakellaridis-Venkatesh in the case at hand.

We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$. Our theorems are based on a comparison of the…

In this paper, we prove one direction of the Gan--Gross--Prasad conjecture on metaplectic-symplectic groups for tempered cases. Furthermore, we also prove one direction of the non-tempered GGP conjecture for residual representations with…

Let $G(F)$ be a split reductive group over a $p$-adic field $F$ and let $(\pi_{St},V)$ be a (generalized) Steinberg representation of $G(F)$. It is known that the space of Iwahori fixed vectors in $V$ is one dimensional. The Iwahori Hecke…

We consider and provide an accurate study for the fractional Zernike functions on the punctured unit disc, generalizing the classical Zernike polynomials and their associated $\beta$-restricted Zernike functions. Mainly, we give the…

We give a combinatorial evaluation of Iwahori Whittaker functions for unramified genuine principal series representations on metaplectic covers of the general linear group over a non-archimedean local field. To describe the combinatorics,…

This paper is a continuation of a previous paper in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper…

This paper studies spherical Whittaker functions for central extensions of reductive groups over local fields. We follow the development of Chinta and Offen to produce a metaplectic Casselman-Shalika formula for tame covers of all…

We introduce and study a one-parameter generalization of the q-Whittaker symmetric functions. This is a family of multivariate symmetric polynomials, whose construction may be viewed as an application of the procedure of fusion from…

In this paper, we prove a conjecture of Wei Zhang on comparison of certain local spherical characters from which we draw some consequences for the Ichino-Ikeda conjecture for unitary groups.

We prove a refinement of the global Gan-Gross-Prasad conjecture proposed by Ichino-Ikeda and N. Harris for unitary groups under some local conditions. We need to assume some expected properties of L-packets and some part of the local…

We will give new applications of quantum groups to the study of spherical Whittaker functions on the metaplectic $n$-fold cover of $GL(r,F)$, where $F$ is a nonarchimedean local field. Earlier Brubaker, Bump, Friedberg, Chinta and Gunnells…

We study Whittaker--Fourier coefficients of automorphic forms on a quasi-split unitary group. We reduce the analogue of the Ichino--Ikeda conjectures to a conjectural local statement using the descent method of Ginzburg--Rallis--Soudry.

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

Geometric zeta functions of Ihara and Hashimoto are generalized to higher rank. The $p$-adic version of the Patterson conjecture is proven.

We establish the Langlands-Shahidi method over a global field of characteristic p. We then focus on the unitary groups and prove global and local Langlands functoriality to general linear groups for generic representations. Main…

We prove a conjecture of Hiraga-Ichino-Ikeda relating formal degrees of square-integrable representations to adjoint gamma factors for symplectic and even orthogonal groups over characteristic zero non-Archimedean local fields. The proof is…

Let F be a non-archimedean local field of characteristic zero. Jacquet, Piatetski-Shapiro and Shalika introduced the notion of newforms for irreducible generic representations of GL_n(F). In this paper, we give an explicit formula for…

Whittaker functions are special functions that arise in $p$-adic number theory and representation theory. They may be defined on representations of reductive groups as well as their metaplectic covering groups: fascinatingly, many of their…