Constant term identities and Poincare polynomials
Abstract
In 1982 Macdonald published his now famous constant term conjectures for classical root systems. This paper begins with the almost trivial observation that Macdonald's constant term identities admit an extra set of free parameters, thereby linking them to Poincare polynomials. We then exploit these extra degrees of freedom in the case of type A to give the first proof of Kadell's orthogonality conjecture---a symmetric function generalisation of the q-Dyson conjecture or Zeilberger-Bressoud theorem. Key ingredients in our proof of Kadell's orthogonality conjecture are the polynomial lemma of Karasev and Petrov, the scalar product for Demazure characters and (0,1)-matrices.
Cite
@article{arxiv.1209.0855,
title = {Constant term identities and Poincare polynomials},
author = {Gyula Karolyi and Alain Lascoux and S. Ole Warnaar},
journal= {arXiv preprint arXiv:1209.0855},
year = {2015}
}
Comments
27 pages. As new application of our main theorem we prove Sills' constant term conjecture (proved previously by Lv, Xin and Zhou) related to Stembridge's first layer formulas for SL(n,C). To appear in Transactions of the AMS