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Quantum Harish-Chandra isomorphism for the double affine Hecke algebra of GL$_n$
[Isomorphisme de Harish-Chandra quantique pour l’algèbre de Hecke affine double de $\mathrm{GL}_n$]
Joshua Jeishing Wen1
1Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Journal de l’École polytechnique — Mathématiques, Tome 13 (2026), pp. 203-254

We prove that for generic parameters, the quantum radial parts map of Varagnolo and Vasserot gives an isomorphism between the spherical double affine Hecke algebra of $\mathrm{GL}_n$ and a quantized multiplicative quiver variety, as defined by Jordan.

Nous prouvons que pour des paramètres génériques, l’application des parties radiales quantiques de Varagnolo et Vasserot donne un isomorphisme entre l’algèbre de Hecke affine double sphérique de $\mathrm{GL}_n$ et une variété carquois multiplicative quantifiée, telle que définie par Jordan.

Reçu le :
Accepté le :
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DOI : 10.5802/jep.326
Classification : 20C08, 33D52, 53D55, 16G20
Keywords: Deformation quantization, double affine Hecke algebras, multiplicative quiver varieties
Mots-clés : Quantification par déformation, algèbre de Hecke affine double, variété carquois multiplicative

Joshua Jeishing Wen  1

1 Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Quantum {Harish-Chandra} isomorphism for the~double affine {Hecke} algebra {of~GL}$_n$},
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Joshua Jeishing Wen. Quantum Harish-Chandra isomorphism for the double affine Hecke algebra of GL$_n$. Journal de l’École polytechnique — Mathématiques, Tome 13 (2026), pp. 203-254. doi: 10.5802/jep.326

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