Constant term identities and Poincaré polynomials

Károlyi, Gyula, Lascoux, Alain and Ole Warnaar, S. (2015) Constant term identities and Poincaré polynomials. Transactions of the American Mathematical Society, 367 10: 6809-6836. doi:10.1090/tran/6119


Author Károlyi, Gyula
Lascoux, Alain
Ole Warnaar, S.
Title Constant term identities and Poincaré polynomials
Journal name Transactions of the American Mathematical Society   Check publisher's open access policy
ISSN 0002-9947
1088-6850
Publication date 2015-08-13
Sub-type Article (original research)
DOI 10.1090/tran/6119
Open Access Status Not Open Access
Volume 367
Issue 10
Start page 6809
End page 6836
Total pages 28
Place of publication Providence, RI, United States
Publisher American Mathematical Society
Collection year 2016
Language eng
Formatted 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 Poincaré 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 multivariable Lagrange interpolation, the scalar product for Demazure characters and (0,1)-matrices.
Keyword (0,1)-matrices
Constant term identities
Kadell’s conjecture
Poincar´e polynomials
Polynomial lemma
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
 
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