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arXiv · 1707.03519

Affine Hecke Algebras via DAHA

Ivan Cherednik
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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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BibTeXRIS

Ivan Cherednik. 2017-07-12. Affine Hecke Algebras via DAHA. https://doi.org/10.1007/s40598-018-0082-5

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