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Affine Hecke Algebras via DAHA

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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.

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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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  1. Department of Mathematics, UNC Chapel Hill, Chapel Hill, NC, 27599, USA

    Ivan Cherednik

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  1. Ivan Cherednik
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Correspondence to Ivan Cherednik.

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Dedicated to Masaki Kashiwara, a great master of harmonic analysis, on the occasion of his 70th birthday..

Partially supported by NSF Grant DMS-1363138.

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Cherednik, I. Affine Hecke Algebras via DAHA. Arnold Math J. 4, 69–85 (2018). https://doi.org/10.1007/s40598-018-0082-5

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  • DOI: https://doi.org/10.1007/s40598-018-0082-5

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