Book Review: Double affine Hecke algebras
DOI10.1090/S0273-0979-08-01208-1zbMath1292.00035MaRDI QIDQ5494736
Jasper V. Stokman, Eric M. Opdam
Publication date: 29 July 2014
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Hecke algebras and their representations (20C08) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) 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) External book reviews (00A17) Research exposition (monographs, survey articles) pertaining to group theory (20-02) Root systems (17B22)
Cites Work
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- Quantum affine algebras and holonomic difference equations
- From double Hecke algebra to Fourier transform
- Orthogonal polynomials associated with root systems
- Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
- Double affine Hecke algebras and Macdonald's conjectures
- Quantum zonal spherical functions and Macdonald polynomials
- Induced representations of double affine Hecke algebras and applications
- Macdonald's evaluation conjectures and difference Fourier transform
- A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras
- On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
- An elementary approach to the hypergeometric shift operators of Opdam
- Affine Hecke Algebras and Their Graded Version
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