Related papers: Unramified Whittaker functions for certain Brylins…

We consider the analog of Gelfand-Graev representations of the uniteriangular group. We obtain the decomposition into the sum of irreducible representations, prove that these representations are multiplicity free, calculate the 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…

We compute generalized Bernstein-Reznikov integrals associated with standard complex symplectic forms by studying Knapp-Stein intertwining operators between spherical degenerate principal series of complex symplectic groups.

We study the TQFT mapping class group representations for surfaces with boundary associated with the $SU(2)$ gauge group, or equivalently the quantum group $U_q(\Sl(2))$. We show that at a prime root of unity, these representations are all…

We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.

This paper is a brief review of recent results on the concept of ``generalized $\tau$-function'', defined as a generating function of all the matrix elements in a given highest-weight representation of a universal enveloping algebra ${\cal…

Analysis of function spaces and special functions are closely related to the representation theory of Lie groups. We explain here the connection between the Laguerre functions, the Laguerre polynomials, and the Meixner-Pollacyck polynomials…

Inspired by Ol'shanskii's work, we provide an axiomatic framework to describe certain irreducible unitary representations of non-discrete unimodular totally disconnected locally compact groups. We then look at the applications to certain…

Whittaker functions of $GL(n, \mathbb R)$ , are most known for its role in the Fourier-Whittaker expansion of cusp forms. Their behavior in the Siegel set, in large, is well-understood. In this paper, we insert into the literature some…

Using quantum representations of mapping class groups we prove that profinite completions of Burnside-type surface group quotients are not virtually prosolvable, in general. Further, we construct infinitely many finite simple characteristic…

We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric $q$-Whittaker functions. In particular, we show that the series part of the nonsymmetric $q$-Whittaker…

The study of Whittaker models for representations of reductive groups over local and global fields has become a central tool in representation theory and the theory of automorphic forms. However, only generic representations have Whittaker…

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…

We study degenerate Whittaker vectors in scalar type holomorphic discrete series representations of tube type Hermitian Lie groups and their analytic continuation. In four different realizations, the bounded domain picture, the tube domain…

We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…

We develop differential and symplectic geometry of differentiable Deligne-Mumford stacks (orbifolds) including Hamiltonian group actions and symplectic reduction. As an application we construct new examples of symplectic toric DM stacks as…

We consider a natural basis of the Iwahori fixed vectors in the Whittaker model of an unramified principal series representation of a split semisimple p- adic group, indexed by the Weyl group. We show that the elements of this basis may be…

Let $X$ be a general cyclic cover of $\mathbb{CP}^{1}$ ramified at $m$ points, $\lambda_1...\lambda_m.$ we define a class of non positive divisors on $X$ of degree $g-1$ supported in the pre images of the branch points on $X$, such that the…

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 determine all irreducible representations of primary quasi-cyclotomic fields in this paper. The methods can be applied to determine the irreducible representations of any quasi-cyclotomic field. We also compute the Artin L-functions for…