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Automorphic representations and Harmonic analysis
Automorphic representations and Harmonic analysis
On locally analytic cohomology in the Steinberg cases
On locally analytic cohomology in the Steinberg cases
Organizers
Speaker
Zicheng Qian
Time
Thursday, October 22, 2026 1:30 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 435 529 7909
(BIMSA)
Abstract
As is often called the "special" case of ($p$ adic or classical) local Langlands correspondence, Steinberg case often simultaneously admits extra difficulty yet also more available tools (or related objects) than other cases. In this talk, we explain a technique on the study of locally analytic Steinberg cases by restriction from $G$ to $(g,N(T))$. Such technique is useful for at least two aspects. First, it reduces the computation of locally analytic cohomology in the Steinberg case to certain corresponding $(g,N(T))$ cohomology which is a mixture of Lie algebra homlogy and smooth $T$ cohomology via the Weyl group. Second, $(g,N(T))$ cohomology offer a natural setting to the discussion of choice of uniformizer/branch of logarithm which is a typical phenomenon for the Steinberg case of LL.