Symmetric and nonsymmetric Macdonald polynomials

DOI10.1007/BF01608794zbMath0942.33012arXivmath/9812080OpenAlexW2062329582MaRDI QIDQ1306611

Dan Marshall

Publication date: 16 August 2000

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9812080

zbMATH Keywords

Macdonald polynomialsJack polynomials\(q\)-Selberg integral

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Nonsymmetric Macdonald polynomials via integrable vertex models, Connections between vector-valued and highest weight Jack and Macdonald polynomials, Properties of the nonsymmetric Robinson-Schensted-Knuth algorithm, Quasisymmetric Schur functions, Jack polynomial fractional quantum Hall states and their generalizations, Further Pieri-type formulas for the nonsymmetric Macdonald polynomial, Dual immaculate quasisymmetric functions expand positively into Young quasisymmetric Schur functions, The norm and the evaluation of the Macdonald polynomials in superspace, S-duality and the \( \mathcal{N}=2 \) Lens space index, Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials, Unnamed Item, From multiline queues to Macdonald polynomials via the exclusion process, From multiline queues to Macdonald polynomials via the exclusion process

Cites Work

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• A proof of Andrews' \(q\)-Dyson conjecture
• Intertwining operators and polynomials associated with the symmetric group
• Integration of quantum many-body problems by affine Knizhnik- Zamolodchikov equations
• A recursion and a combinatorial formula for Jack polynomials
• Constant term identities of Forrester-Zeilberger-Cooper
• Binomial formula for Macdonald polynomials and applications
• Generalizations of the \(q\)-Morris constant term identity
• Isomorphisms of type \(A\) affine Hecke algebras and multivariable orthogonal polynomials
• Euler-Poincaré characteristic and polynomial representations of Iwahori-Hecke algebras
• Dynamical correlation functions and finite-size scaling in the Ruijsenaars-Schneider model
• A reproducing kernel for nonsymmetric Macdonald polynomials
• Affine Hecke algebras and raising operators for Macdonald polynomials
• A Proof of Askey’s Conjectured q-Analogue of Selberg’s Integral and a Conjecture of Morris
• A Short Proof of MacDonald's Conjecture for the Root Systems of Type A
• Une q-Intégrale de Selberg et Askey
• Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews
• $q$-Selberg integrals and Macdonald polynomials
• Multivariable Al-Salam & Carlitz Polynomials Associated with the TypeA q-Dunkl Kernel