Related papers: Whittaker functions and Demazure characters
A combinatorial formula to generate U(N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated.…
This paper builds on earlier work, where the authors described Whittaker modules for the Virasoro algebra. Using a framework of Batra and Mazorchuk, the current paper investigates a category of Virasoro algebra modules that includes…
These notes are a part of my lectures on representations of adelic groups attached to two-dimensional schemes. They contain a study of the one-dimensional case as a preliminary step to the case of dimension two. We consider the following…
Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum, was developed. This distribution function is…
We find an explicit closed formula for the $k$'th iterated commutator $\mathrm{ad}_A^k(H_V(\xi))$ of arbitrary order $k\ge1$ between a Hamiltonian $H_V(\xi)=M_{\omega_\xi}+S_{\check V}$ and a conjugate operator…
There is a q-deformation of the reflection representation of the affine symmetric group, which arises in the quantum geometric Satake equivalence, and in the study of the complex reflection groups $G(m,m,n)$. Demazure operators (often…
In this article, the concept of $\mu-$ monotonic property of interval-valued function in higher dimension is introduced. Expansion of interval-valued function in higher dimension is developed using this property. Generalized Hukuhara…
In this paper, we investigate the ``shuffle-type'' formula for special values of desingularized multiple zeta functions at integer points. It is proved by giving an iterated integral/differential expression for the desingularized multiple…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
The Mittag-Leffler type functions arise naturally in the solution of fractional order integral and differential equations, especially in the investigations of the fractional generalization of the kinetic equation. This article introduces a…
The paper studies how to compute irreducible characters of the generalized symmetric group $C_k\wr{S}_n$ by iterative algorithms. After reproving the Ariki-Koike version of the Murnaghan-Nakayama rule by vertex algebraic methods, we…
We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group $\rm{Spin}_{2r+1}({\mathbb C})$, which is an analogue of the formulas of Tokuyama for Schur…
We establish a super Frobenius formula for the characters of Iwahori-Hecke algebras. We show that the Hall-Littlewood sypersymmetric function, up to constant, generates the values of the irreducible characters of Iwahori-Hecke algebras at…
Let h^{*} be a multiplicative cohomology theory, h_{*} its dual homology theory and \hat{h}^{*} a differential refinement. We first construct the natural pairing between h_{*} and the flat part of \hat{h}^{*}, generalizing the holonomy of a…
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…
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…
The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…
Let $p$ be an odd prime. Consider normalized newforms $f_1,f_2$ that both satisfy the Heegner hypothesis for an imaginary quadratic field $K$ and suppose that they induce isomorphic residual Galois representations. In the work of…
The paper discusses some properties of the modulus $|W_{k,m}(z)|$ of the Whittaker function $W_{k,m}(z)$. In particular, completely monotone functions expressed in terms of $|W_{k,m}(z)|$ are found. The results follow from an integral…
In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the…