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Involutions of Double Affine Hecke Algebras

Published online by Cambridge University Press:  04 December 2007

Bogdan Ion
Bogdan Ion
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ-08544, U.S.A. e-mail: bogdan@math.princeton.edu
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Abstract

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We prove the existence of an involution on double affine Hecke algebras. This involution plays a central role in the theory of Macdonald polynomials, being responsible for a Fourier type duality and allowing the construction of affine intertwiners.

Keywords

Artin groupfundamental groupHecke algebraMacdonald polynomialsregular orbits space
Type
Research Article
Information
Compositio Mathematica , Volume 139 , Issue 1 , October 2003 , pp. 67 - 84
Copyright
© 2003 Kluwer Academic Publishers