Connection coefficients for basic Harish-Chandra series
Abstract
Basic Harish-Chandra series are asymptotically free meromorphic solutions of the system of basic hypergeometric difference equations associated to root systems. The associated connection coefficients are explicitly computed in terms of Jacobi theta functions. We interpret the connection coefficients as the transition functions for asymptotically free meromorphic solutions of Cherednik's root system analogs of the quantum Knizhnik-Zamolodchikov equations. They thus give rise to explicit elliptic solutions of root system analogs of dynamical Yang-Baxter and reflection equations. Applications to quantum c-functions, basic hypergeometric functions, reflectionless difference operators and multivariable Baker-Akhiezer functions are discussed.
Cite
@article{arxiv.1208.6145,
title = {Connection coefficients for basic Harish-Chandra series},
author = {Jasper V. Stokman},
journal= {arXiv preprint arXiv:1208.6145},
year = {2014}
}
Comments
34 pages. In the second version some additional references are included. In third version a typo in formula (1.10) is corrected, and references are updated