Macdonald's polynomials and representations of quantum groups

DOI10.4310/MRL.1994.v1.n3.a1zbMath0833.17007arXivhep-th/9312103MaRDI QIDQ1901656

Pavel I. Etingof, Alexander A. jun. Kirillov

Publication date: 12 March 1996

Published in: Mathematical Research Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9312103

zbMATH Keywords

quantum grouprepresentationMacdonald's polynomialsorthogonal symmetric polynomialsweighted traces of intertwining operators

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items

\(S\)-functions, spectral functions of hyperbolic geometry, and vertex operators with applications to structure for Weyl and orthogonal group invariants, Nonsymmetric Macdonald polynomials via integrable vertex models, On the affine analogue of Jack and Macdonald polynomials, Spherical functions on affine Lie groups, Macdonald's evaluation conjectures and difference Fourier transform, Integral formulas for wave functions of quantum many-body problems and representations of 𝔤l n, The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems, Poisson-Lie interpretation of trigonometric Ruijsenaars duality, Bispectral quantum Knizhnik-Zamolodchikov equations for arbitrary root systems, Shapovalov elements of classical and quantum groups, On \(q\)-deformed \({\mathfrak{gl}_{\ell+1}}\)-Whittaker function. I, Hopf dreams and diagonal harmonics, A new integral formula for Heckman-Opdam hypergeometric functions, Asymptotic formulas for Macdonald polynomials and the boundary of the \((q,t)\)-Gelfand-Tsetlin graph, \(q\)-deformations of two-dimensional Yang-Mills theory: classification, categorification and refinement, Connection coefficients for basic Harish-Chandra series, New compact forms of the trigonometric Ruijsenaars-Schneider system, Genus two generalization of \(A_1\) spherical DAHA, Hilbert schemes, polygraphs and the Macdonald positivity conjecture, Lectures on affine Hecke algebras and Macdonald’s conjectures, Affine Macdonald conjectures and special values of Felder-Varchenko functions, Difference Hierarchies for nT τ-functions, An algebraic approach to Macdonald–Koornwinder polynomials: Rodrigues-type formula and inner product identity, h-Transforms and Orthogonal Polynomials, Double affine Hecke algebras at roots of unity, Adler–Kostant–Symes scheme for face and Calogero–Moser–Sutherland-type models, Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction, Canonical basis and Macdonald polynomials, Laumon spaces and the Calogero-Sutherland integrable system, Elliptic quantum groups and Ruijsenaars models, Colorful combinatorics and Macdonald polynomials, Unnamed Item, On Cherednik-Macdonald-Mehta identities, Traces of intertwiners for quantum groups and difference equations. I, Orthogonality and the qKZB-heat equation for traces of \(U_q({\mathfrak g})\)-intertwiners, Macdonald polynomials and algebraic integrability