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Affine Hecke Algebras via DAHA

Affine Hecke Algebras via DAHA 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 $$A_1$$ A 1 in the spherical case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

Affine Hecke Algebras via DAHA

Cherednik, Ivan
Arnold Mathematical Journal , Volume 4 (1) – Apr 3, 2018
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17 pages

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
Subject
Mathematics; Mathematics, general
ISSN
2199-6792
eISSN
2199-6806
DOI
10.1007/s40598-018-0082-5
Publisher site
See Article on Publisher Site

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 $$A_1$$ A 1 in the spherical case.

Journal

Arnold Mathematical Journal – Springer Journals

Published: Apr 3, 2018

References

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