\(R\)-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators

DOI10.1007/BF02099422zbMath0820.17023OpenAlexW2076291133MaRDI QIDQ1338878

Shin-Ichi Kato

Publication date: 18 December 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099422

zbMATH Keywords

\(R\)-matricesaffine Hecke algebraaffine root systemKnizhnik- Zamolodchikov equationsMacdonald's difference operators

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) PDEs in connection with quantum mechanics (35Q40)

Related Items

QKZ-Ruijsenaars correspondence revisited, Bispectral quantum Knizhnik-Zamolodchikov equations for arbitrary root systems, Connection coefficients for basic Harish-Chandra series, A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type, Yang-Baxter basis of Hecke algebra and Casselman's problem (extended abstract)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Factorizing particles on a half-line and root systems
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Quantum affine algebras and holonomic difference equations
• Quantum Knizhnik-Zamolodchikov equations and affine root systems
• Integrable connections related to zonal spherical functions
• Analyse harmonique dans les systèmes de Tits bornologiques de type affine
• The Poincaré series of a Coxeter group
• On the Kazhdan-Lusztig polynomials for affine Weyl groups
• Affine root systems and Dedekind's \(\eta\)-function
• Affine Hecke Algebras and Their Graded Version