Nonsymmetric Difference Whittaker Functions and Double Affine Hecke Algebras

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Orr, Daniel
- Affiliation: College of Arts and Sciences, Department of Mathematics

Abstract

This dissertation is devoted to a new theory of nonsymmetric difference Whittaker functions and the corresponding Toda-Dunkl operators for arbitrary reduced irreducible root systems. The nonsymmetric Whittaker functions are obtained as limits of (global) spherical functions under a variant of a limiting procedure due to Ruijsenaars and Etingof. Under this procedure, the Toda-Dunkl operators are realized as limits of difference-reflection Dunkl operators. We give a direct and constructive proof of the existence of these limits. We show that the nonsymmetric Whittaker function solves the eigenvalue problem for Toda-Dunkl operators and admits an explicit expansion in terms of the level-one affine Demazure characters.

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