Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series
Combinatorics
2011-12-15 v1 Classical Analysis and ODEs
Abstract
A one-parameter generalisation R_{\lambda}(X;b) of the symmetric Macdonald polynomials and interpolations Macdonald polynomials is studied from the point of view of branching rules. We establish a Pieri formula, evaluation symmetry, principal specialisation formula and q-difference equation for R_{\lambda}(X;b). We also prove a new multiple q-Gauss summation formula and several further results for sl_n basic hypergeometric series based on R_{\lambda}(X;b).
Cite
@article{arxiv.0903.3996,
title = {Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series},
author = {Alain Lascoux and S. Ole Warnaar},
journal= {arXiv preprint arXiv:0903.3996},
year = {2011}
}
Comments
28 pages