A new take on spherical, Whittaker and Bessel functions (Spherical and Whittaker functions via DAHA I,II)
Abstract
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.
Keywords
Cite
@article{arxiv.0904.4324,
title = {A new take on spherical, Whittaker and Bessel functions (Spherical and Whittaker functions via DAHA I,II)},
author = {Ivan Cherednik and Xiaoguang Ma},
journal= {arXiv preprint arXiv:0904.4324},
year = {2012}
}
Comments
v4: further improvements of the theory of affine symmetrizers, editing; v5: improving refferences, editing; v6: a somewhat extended version of v5 essentially equivalent to the papers "Spherical and Whittaker Functions via DAHA I,II" to be published by Selecta Mathematica