0. Introduction 5 0.1. Objectives and main results 5 0.1.1. Affine Satake isomorphisms 5 0.1.2. Whittaker functions 6 0.1.3. The setting of the paper 7 0.2. Dunkl operators via DAHA 7 0.2.1. Families of Dunkl operators 8 0.3. The technique of spinors 9 0.3.1. Connections to AKZ 9 0.3.2. Isomorphism theorems 10 0.3.3. The localization functor 10 0.3.4. The Whittaker limit 11 0.4. On Langlands’ p...

In the present paper, we define a new representation for Voigt function involving the product of generalized Bessel function and Whittaker function. We first obtain its explicit representation and then we derive partly bilateral and partly unilateral representations for this function. Further, we establish some new and interesting generating functions involving various hypergeometric functions ...

We introduce and study a one-parameter generalization of the q –Whittaker symmetric functions. This is family multivariate polynomials, whose construction may be viewed as an application procedure fusion from integrable lattice models to vertex model interpretation Hall–Littlewood polynomials [3] , [6] [7] . prove branching Pieri rules, standard dual (skew) Cauchy summation identities, integral...

We prove a localization theorem for affine W-algebras in the spirit of Beilinson–Bernstein and Kashiwara–Tanisaki. More precisely, any non-critical regular weight λ, we identify λ-monodromic Whittaker D-modules on enhanced flag variety with full subcategory Category O W-algebra. To essential image our functor, provide new realization using Iwahori–Whittaker modules corresponding Kac–Moody algeb...

We address the problem of simulating an arbitrary binary interactive first-order Markovian protocol over a pair of binary symmetric channels with crossover probability ε. We are interested in the achievable rates of reliable simulation, i.e., in characterizing the smallest possible blowup in communications such that a vanishing error probability (in the protocol length) can be attained. Whereas...

Recently, the convolution of the sinc kernel with the infinite sequence of a periodic function was expressed as a finite summation. The expression obtained, however, is not numerically stable when evaluated at or near integer values of time. This correspondence presents a numerically stable formulation equivalent to the results reported in the above cited paper and which, when sampled, is also ...