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arXiv · 1901.11077

Construction of Sheaves of Cherednik Algebras via Formal Geometry

Alexander Vitanov
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Abstract

In this note we realize the sheaf of Cherednik algebras $H_{1, c, X, G}$ on a general good complex orbifold $X/G$, originally introduced by Etingof for smooth complex varieties with an action by a finite group, by gluing sheaves of flat sections of flat holomorphic vector bundles on orbit type strata in $X$ which result from a localization procedure. In the case, when $c$ is formal, this construction can be interpreted as a formal deformation of $D_X\rtimes\mathbb CG$ via Gel'fand-Kazhdan formal geometry. Contrary to the original definition of $H_{1, c, X, G}$ the presented construction permits the computation of trace densities, Hochschild homologies and an algebraic index theorem for formal deformations of $D_X\rtimes\mathbb CG$. We also hope that the methods developed here will contribute towards a full proof of Dolgushev-Etingof's conjecture.

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Alexander Vitanov. 2022-06-20. Construction of Sheaves of Cherednik Algebras via Formal Geometry. https://arxiv.org/abs/1901.11077

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