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

Abstract

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 $SL(n,\mathbb{C})$.

21 pages

References in corpus (1)

• Disturbing the Dyson conjecture in a \emph{generally} GOOD way

Cited by in corpus (1)

• Two Coefficients of the Dyson Product