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Arnold Mathematical Journal

, Volume 4, Issue 1, pp 69–85 | Cite as

Affine Hecke Algebras via DAHA

  • Ivan Cherednik
Research Contribution

Abstract

A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation necessary here is a generalization of “picking up residues” due to Arthur, Heckman, Opdam and others, which can be traced back to Hermann Weyl. Generally, it is a finite sum of integrals over double affine residual subtori; a complete formula is presented for \(A_1\) in the spherical case.

Keywords

Hecke algebras Fourier transform Spherical functions Plancherel measure Nonsymmetric Macdonald polynomials 

Notes

Acknowledgements

The author thanks RIMS, Kyoto university for the invitation, and the participants of his course at UNC. Many thanks to the referee for important remarks.

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Copyright information

© Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2018

Authors and Affiliations

  1. 1.Department of MathematicsUNC Chapel HillChapel HillUSA

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