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math.RT2026
Relative Serre duality for Hecke categories
Quoc P. Ho, Penghui Li
We prove a conjecture of Gorsky, Hogancamp, Mellit, and Nakagane in the Weyl group case. Namely, we show that the left and right adjoints of the parabolic induction functor between…
math.RT2025
Graded character sheaves, HOMFLY-PT homology, and Hilbert schemes of points on
Quoc P. Ho, Penghui Li
Using a geometric argument building on our new theory of graded sheaves, we compute the categorical trace and Drinfel'd center of the (graded) finite Hecke category $\mathsf{H}_W^\…
math.RT2024
Functions on the commuting stack via Langlands duality
Penghui Li, David Nadler, Zhiwei Yun
We calculate the dg algebra of global functions on commuting stacks of complex reductive groups using tools from Betti Geometric Langlands. In particular, we prove that the ring of…