A Family of $q$-Dyson Style Constant Term Identities

Details A Family of $q$-Dyson Style Constant Term Identities A Family of $q$-Dyson Style Constant Term Identities

2007-06-07

arxiv.org/abs/0706.1009v1

Mathematics

Commutative Algebra

21 pages

Scientific paper

By generalizing Gessel-Xin's Laurent series method for proving the Zeilberger-Bressoud $q$-Dyson Theorem, we establish a family of $q$-Dyson style constant term identities. These identities give explicit formulas for certain coefficients of the $q$-Dyson product, including three conjectures of Sills' as special cases and generalizing Stembridge's first layer formulas for characters of $SL(n,\mathbb{C})$.

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