Mathematics > Representation Theory
arXiv:2606.22747 (math)
[Submitted on 22 Jun 2026]
Abstract:We discuss the action of the center in the categorical local Langlands program in the form of [FS24].
We provide a spectral description of the convolution action of a central torus in this situation.
We show that the veracity of the $\ell$-adic categorical Langlands conjecture passes to the quotient by a central torus $D$ satisfying a minor cohomological condition in characteristic 0 and we show that under restriction to Langlands-Shahidi type parameters the conjecture passes to such a quotient in all characterstics and even integrally.
In that situation we also show that the splitting of the semi-orthogonal decomposition descends.
Finally we use these results to extend [Zou25] to $\mathrm{PGL}_n$.
Submission history
From: Konrad Zou [view email]
[v1]
Mon, 22 Jun 2026 01:28:03 UTC (32 KB)
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