A new take on spherical, Whittaker and Bessel functions

Details A new take on spherical, Whittaker and Bessel functions A new take on spherical, Whittaker and Bessel functions

2009-04-28

arxiv.org/abs/0904.4324v5

Mathematics

Quantum Algebra

112 pgs; v2: the theory of affine DAHA symmetrizers is improved (convergence of the coefficients, the rank one case), editing;

Scientific paper

This paper is based on the lectures given by the first author at Harvard in February and March, 2009. It begins with an introduction to the classical p-adic theory of the Macdonald, Matsumoto and Whittaker functions. Its major directions are as follows: 1) extending the theory of DAHA to arbitrary levels; 2) the affine Satake isomorphism and Hall functions via DAHA; 3) the spinor Dunkl operators for the Q-Toda equation; 4) applications to the nil-DAHA and Q-Whittaker functions; 5) the technique of spinors in the differential theory and its applications to the AKZ-QMBP isomorphism theorem.

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