arXiv subjects

Yau Wing Li

Publications and source records attributed to Yau Wing Li.

3 recordsLinked to original sources

arXiv2025

Endoscopy for affine Hecke categories

We show that the neutral block of the affine monodromic Hecke category for a reductive group is monoidally equivalent to the neutral block of the affine Hecke category for the endoscopic group. The semisimple complexes of both categories can be identified with the generalized Soergel bimodules via the Soergel functor. We extend this identification of semisimple complexes to the neutral blocks of the affine Hecke categories by the technical machinery developed by Bezrukavnikov and Yun.

math.RT↗

arXiv2025

Endoscopy for metaplectic affine Hecke categories

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.

math.RT↗

arXiv2025

Matchings in Corona graph and classical symmetric varieties

We introduce an alternative combinatorial parametrization of Borel orbits in classical symmetric varieties using matchings of the Corona graph. As an application, we obtain ultra log-concavity and unimodality for the number of Borel orbits in Types AIII and CII. Moreover, we prove a conjecture of Can and Ugurlu concerning the non-integrality of the coefficients of the polynomial that interpolates the number of orbits in Type BI.

math.CO↗