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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2015

Constant term identities and Poincaré polynomials

Résumé

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.

Dates et versions

hal-00826213 , version 1 (27-05-2013)

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Gyula Karolyi, Alain Lascoux, S. Ole Warnaar. Constant term identities and Poincaré polynomials. Transactions of the American Mathematical Society, 2015, 367, pp.6809-6836. ⟨10.1090/tran/6119⟩. ⟨hal-00826213⟩
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