Related papers: On Iwahori-Whittaker Functions for Metaplectic Gro…

We introduce the (global) q-Whittaker function as the limit at t=0 of the q,t-spherical function extending the symmetric Macdonald polynomials to arbitrary eigenvalues. The construction heavily depends on the technique of the q-Gaussians…

For an arbitrary split adjoint group we identify the unramified Whittaker space with the space of skew-invariant functions on the lattice of coweights and deduce from it the Casselman-Shalika formula.

In this paper, we extend results connecting quantum groups to spherical Whittaker functions on metaplectic covers of $GL_r(F)$, for $F$ a nonarchimedean local field. Brubaker, Buciumas, and Bump showed that for a certain metaplectic…

We prove the Casselman-Shalika formula for unramified groups over a non-archimedean local field by studying the action of the spherical Hecke algebra on the space of compact spherical Whittaker functions via the twisted Satake transform.…

There are few constructions of square-integrable automorphic functions on metaplectic groups. Such functions may be obtained by the residues of certain Eisenstein series on covers of groups, "theta functions," but the Fourier coefficients…

In this work we study the relationship between several combinatorial formulas for type $A$ spherical Whittaker functions. These are spherical functions on $p$-adic groups, which arise in the theory of automorphic forms. They depend on a…

We describe the structure of the Whittaker or Gelfand-Graev module on a $n$-fold metaplectic cover of a $p$-adic group $G$ at both the Iwahori and spherical level. We express our answer in terms of the representation theory of a quantum…

We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However…

We state and prove a formula for the Whittaker-Shintani functions associated to Fourier-Jacobi models for p-adic unitary groups and general linear groups. These generalized spherical functions play a fundamental role in the proof of the…

We present a new framework for a broad class of affine Hecke algebra modules, and show that such modules arise in a number of settings involving representations of $p$-adic groups and $R$-matrices for quantum groups. Instances of such…

For Iwahori-spherical representations of non-Archimedean general linear groups, Chan-Savin recently expressed the Whittaker functor as a restriction to an isotypic component of a finite Iwahori-Hecke algebra module. We generalize this…

We computed the first Whittaker coefficient of an Eisenstein series on a global metaplectic group induced from the torus and related the result with a Weyl group multiple Dirichlet series attached to the (dual) root system of the group…

Chinta and Gunnells introduced a rather intricate multi-parameter Weyl group action on rational functions on a torus, which, when the parameters are specialized to certain Gauss sums, describes the functional equations of Weyl group…

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of…

Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…

Weyl group multiple Dirichlet series, introduced by Brubaker, Bump, Chinta, Friedberg and Hoffstein, are expected to be Whittaker coefficients of Eisenstein series on metaplectic groups. Chinta and Gunnells constructed these multiple…

We prove the Plancherel formula for Whittaker functions on a reductive p-adic group. This a sequel to our work on Paley-Wiener theorem. Our proof is close to the proof written by Waldspurger of the Harish-Chandra Plancherel formula for…

We convolve a theta function on an $n$-fold cover of $GL_3$ with an automorphic form on an $n'$-fold cover of $GL_2$ for suitable $n,n'$. To do so, we induce the theta function to the $n$-fold cover of $GL_4$ and use a Shalika integral. We…

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 present generating functions for extensions of multiplicative invariants of wreath symmetric products of orbifolds presented as the quotient by the locally free action of a compact, connected Lie group in terms of orbifold sector…