Affine Springer Fibers, Procesi bundles, and Cherednik algebras

2021/04/19 by Pablo Boixeda Alvarez, Alvarez, Pablo Boixeda, Ivan Losev +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2104.09543

Abstract

Let \mathfrakg be a semisimple Lie algebra, \mathfrakt its Cartan subalgebra and W the Weyl group. The goal of this paper is to prove an isomorphism between suitable completions of the equivariant Borel-Moore homology of certain affine Springer fibers for \mathfrakg and the global sections of a bundle related to a Procesi bundle on the smooth locus of a partial resolution of (\mathfrakt⊕ \mathfrakt^*)/W. We deduce some applications of our isomorphism including a conditional application to the center of the small quantum group. Our main method is to compare certain bimodules over rational and trigonometric Cherednik algebras.

Citations

• Etingof conjecture for quantized quiver varieties

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