Bisymmetric functions, Macdonald polynomials and sl_3 basic hypergeometric series
Combinatorics
2008-05-21 v2 Quantum Algebra
Abstract
A new type of sl_3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl_3 basic hypergeometric series is a bisymmetric function related to Macdonald's commuting family of q-difference operators, to the sl_3 Selberg integrals of Tarasov and Varchenko, and to alternating sign matrices. Our main result for sl_3 series is a multivariable generalization of the celebrated q-binomial theorem. In the limit this q-binomial sum yields a new sl_3 Selberg integral for Jack polynomials.
Cite
@article{arxiv.math/0511333,
title = {Bisymmetric functions, Macdonald polynomials and sl_3 basic hypergeometric series},
author = {S. Ole Warnaar},
journal= {arXiv preprint arXiv:math/0511333},
year = {2008}
}
Comments
33 pages; major revision of earlier, much longer paper; to appear in Compositio Mathematica