Double Affine Hecke Algebras and Bispectral Quantum Knizhnik-Zamolodchikov Equations

DOI10.1093/imrn/rnp165zbMath1200.32012arXiv0812.1005OpenAlexW3100593778MaRDI QIDQ3552255

Michel van Meer, Jasper V. Stokman

Publication date: 14 April 2010

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.1005

zbMATH Keywords

affine Weyl groupMacdonald polynomialsdouble affine Hecke algebrascentral characterKnizhnik-Zamolodchikov equations\(q\)-difference operators and equationsbispectral quantum KZ equationsmeromorphic self-dual solutionself-dual Harish-Chandra series solutionsymmetric self-dual Laurent polynomial solutions

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Difference equations, scaling ((q)-differences) (39A13) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (9)

Construction of eigenfunctions for the elliptic Ruijsenaars difference operators ⋮ Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions ⋮ Integrability of conformal blocks. I: Calogero-Sutherland scattering theory ⋮ Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations ⋮ One-dimensional nil-DAHA and Whittaker functions. I. ⋮ Bispectral quantum Knizhnik-Zamolodchikov equations for arbitrary root systems ⋮ Connection coefficients for basic Harish-Chandra series ⋮ Dualities in quantum integrable many-body systems and integrable probabilities. I. ⋮ Connection problems for quantum affine KZ equations and integrable lattice models

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