One-dimensional double Hecke algebra and Gaussian sums

DOI10.1215/S0012-7094-01-10834-XzbMath1007.11050OpenAlexW1995238668MaRDI QIDQ1847847

Ivan V. Cherednik

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-10834-x

zbMATH Keywords

Verlinde algebradouble affine Hecke algebra\(q\)-Gauss integralGauss-Selberg sum

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Gauss and Kloosterman sums; generalizations (11L05) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Nevanlinna theory of the Askey-Wilson divided difference operator, Hyperbolic beta integrals, An expansion formula for the Askey-Wilson function

Cites Work

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• Some applications of hypergeometric shift operators
• The Dunkl transform
• The big \(q\)-Jacobi function transform
• Harmonic analysis for certain representations of graded Hecke algebras
• An elementary approach to the hypergeometric shift operators of Opdam
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Tensor Structures Arising from Affine Lie Algebras. III
• A new class of symmetric functions