Spherical and Whittaker functions via DAHA. II.

DOI10.1007/s00029-012-0116-0zbMath1293.20006arXiv0904.4324OpenAlexW4237051572MaRDI QIDQ361797

Xiaoguang Ma, Ivan V. Cherednik

Publication date: 19 August 2013

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.4324

zbMATH Keywords

spherical functionsBessel functionsMacdonald polynomialsKnizhnik-Zamolodchikov equationWhittaker functionsdouble affine Hecke algebrasquantum many-body problemToda operators

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Hecke algebras and their representations (20C08) Analysis on (p)-adic Lie groups (22E35) 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) Analysis on and representations of infinite-dimensional Lie groups (22E66)

Related Items

Generalized Weyl modules and nonsymmetric \(q\)-Whittaker functions ⋮ Hecke modules from metaplectic ice ⋮ One-dimensional nil-DAHA and Whittaker functions. II. ⋮ Extremal part of the PBW-filtration and nonsymmetric Macdonald polynomials ⋮ Nonsymmetric difference Whittaker functions

Cites Work

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• Spherical and Whittaker functions via DAHA. I.
• Double affine Hecke algebra in logarithmic conformal field theory
• On \(q\)-deformed \(\mathfrak{gl}_{\ell+1}\)-Whittaker function. III
• Quantum groups at roots of 1
• T-equivariant K-theory of generalized flag varieties
• Twisted Whittaker model and factorizable sheaves
• The quantum dilogarithm and representations of quantum cluster varieties
• Intertwining operators of double affine Hecke algebras
• Integrable connections related to zonal spherical functions
• Integration of quantum many-body problems by affine Knizhnik- Zamolodchikov equations
• Residue construction of Hecke algebras
• On the category \(\mathcal O\) for rational Cherednik algebras.
• On the connection between Macdonald polynomials and Demazure characters
• Another realization of the category of modules over the small quantum group
• Nonsymmetric Macdonald polynomials and Demazure characters.
• Modular transformations for tensor categories
• Elliptic quantum many-body problem and double affine Knizhnik- Zamolodchikov equation
• Harmonic analysis for certain representations of graded Hecke algebras
• Induced representations of double affine Hecke algebras and applications
• An equivalence of fusion categories
• Finite-difference representations of the degenerate affine Hecke algebra
• Nonsemisimple Macdonald polynomials
• Trigonometric Cherednik algebra at critical level and quantum many-body problems
• Quantum Affine Knizhnik-Zamolodchikov Equations and Quantum Spherical Functions, I
• Affine Hecke Algebras and Their Graded Version
• Equivariant Satake category and Kostant-Whittaker reduction
• Whittaker Limits of Difference Spherical Functions
• Differential-Difference Operators Associated to Reflection Groups
• Tensor Structures Arising from Affine Lie Algebras. III
• A limit transition from the Heckman-Opdam hypergeometric functions to the Whittaker functions associated with root systems