\(q\)-Selberg integrals and Macdonald polynomials

DOI10.1007/s11139-005-4849-7zbMath1086.33018OpenAlexW2110598873MaRDI QIDQ2583525

S. Ole Warnaar

Publication date: 17 January 2006

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-005-4849-7

zbMATH Keywords

symmetric functionsSelberg integrals

Mathematics Subject Classification ID

(q)-gamma functions, (q)-beta functions and integrals (33D05) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Basic hypergeometric integrals and functions defined by them (33D60)

Related Items (22)

A new \(q\)-Selberg integral, Schur functions, and Young books ⋮ Remarks on the paper ``skew Pieri rules for Hall-Littlewood functions by Konvalinka and Lauve ⋮ Connection formula for the Jackson integral of type \(A_n\) and elliptic Lagrange interpolation ⋮ A Selberg integral for the Lie algebra \(A_n\) ⋮ A bilateral extension of the $q$-Selberg integral ⋮ Selberg integral theory and Muttalib-Borodin ensembles ⋮ The AFLT \(q\)-Morris constant term identity ⋮ \(q\)-deformations of two-dimensional Yang-Mills theory: classification, categorification and refinement ⋮ 2d-4d connection between \(q\)-Virasoro/\(W\) block at root of unity limit and instanton partition function on ALE space ⋮ The importance of the Selberg integral ⋮ \(q\)-difference systems for the Jackson integral of symmetric Selberg type ⋮ On \(q\)-integrals over order polytopes ⋮ Hilbert spaces of holomorphic functions on generalized Cartan–Hartogs domains ⋮ AFLT-type Selberg integrals ⋮ Branching rules for symmetric functions and \(\mathfrak{sl}_n\) basic hypergeometric series ⋮ The \({\mathfrak{sl}}_3\) Selberg integral ⋮ Hook length property of \(d\)-complete posets via \(q\)-integrals ⋮ Discrete analogues of Macdonald-Mehta integrals ⋮ On a Selberg-Schur integral ⋮ Lecture hall tableaux ⋮ \(q\)-Selberg integrals and Koornwinder polynomials ⋮ Bounded Littlewood identities

Cites Work

• A \(_1\Psi_1\) summation theorem for Macdonald polynomials
• Constant term identities of Forrester-Zeilberger-Cooper
• The Selberg-Jack symmetric functions
• Transformation formulas for multivariable basic hypergeometric series
• A Proof of Some q-Analogues of Selberg’s Integral for $k=1$
• A Proof of Askey’s Conjectured q-Analogue of Selberg’s Integral and a Conjecture of Morris
• Une q-Intégrale de Selberg et Askey
• Ramanujan's Extensions of the Gamma and Beta Functions
• Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews
• A Class of Generalized Hypergeometric Functions in Several Variables
• $q$-Selberg integrals and Macdonald polynomials
• A simple proof of an Aomoto-type extension of Askey's last conjectured Selberg \(q\)-integral
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