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arXiv · 2407.07679

Harish-Chandra isomorphism for cyclotomic double affine Hecke algebras

Joshua Jeishing Wen
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Abstract

We confirm a conjecture of Braverman--Etingof--Finkelberg that the spherical subalgebra of their cyclotomic double affine Hecke algebra (DAHA) is isomorphic to a quantized multiplicative quiver variety for the cyclic quiver, as defined by Jordan. The isomorphism is constructed as a q-analogue of Oblomkov's cyclotomic radial parts map for the rational case. In the appendix, we also prove that the spherical cyclotomic DAHA is isomorphic to the image of a shifted quantum toroidal algebra under Tsymbaliuk's GKLO homomorphism.

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Joshua Jeishing Wen. 2024-10-21. Harish-Chandra isomorphism for cyclotomic double affine Hecke algebras. https://arxiv.org/abs/2407.07679

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