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arXiv · 2412.17525

On Harish-Chandra's Isomorphism

Eric Opdam·Valerio Toledano-Laredo
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Abstract

This is the text of a talk given by the first author at the Harish-Chandra centenary meeting held in Allahabad in October 2023. It reviews Harish-Chandra's isomorphism and its many applications to representation theory and mathematical physics. It also announces the existence and uniqueness of nonsymmetric shift operators for an arbitrary root system. These are differential-reflection operators with a transmutation property relative to Dunkl-Cherednik operators: they shift the parameter k of these operators by 1, and restrict on symmetric functions to the hypergeometric shift operators introduced by the first author.

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Eric Opdam, Valerio Toledano-Laredo. 2024-12-23. On Harish-Chandra's Isomorphism. https://arxiv.org/abs/2412.17525

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