Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Dhillon, Gurbir, Li, Yau Wing, Yun, Zhiwei, Zhu, Xinwen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414425459
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