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arXiv · 2507.16667

Endoscopy for metaplectic affine Hecke categories

Gurbir Dhillon·Yau Wing Li·Zhiwei Yun·Xinwen Zhu
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Abstract

For a possibly twisted loop group $LG$, and any character sheaf of its Iwahori subgroup, we identify the associated affine Hecke category with a combinatorial category of Soergel bimodules. In fact, we prove such results for affine Hecke categories arising from central extensions of the loop group $LG$. Our results work for mod $\ell$ or integral $\ell$-adic coefficients. As applications, we obtain endoscopic equivalences between affine Hecke categories, including the derived Satake equivalence for metaplectic groups, and a series of conjectures by Gaitsgory in quantum geometric Langlands.

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BibTeXRIS

Gurbir Dhillon, Yau Wing Li, Zhiwei Yun, Xinwen Zhu. 2025-07-22. Endoscopy for metaplectic affine Hecke categories. https://arxiv.org/abs/2507.16667

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