Inverse Harish-Chandra Transform and Difference Operators

1997/06/12 by Ivan Cherednik, Cherednik, Ivan
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9706010

openalex publication_date 1997/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply a new technique based on double affine Hecke algebras to the Harish-Chandra theory of spherical zonal functions. The formulas for the Fourier transforms of the multiplications by the coordinates are obtained as well as a simple proof of the Harish-Chandra inversion theorem using the Opdam transform.

Related

• Harish-Chandra decomposition for zonal spherical functions of type A_n
• Introduction to double Hecke algebras
• On generalization of a theorem of Harish-Chandra
• Fourier Transform of Schwartz Algebras on Groups in the Harish-Chandra class
• The dual horospherical Radon transform for polynomials