Free monodromic Hecke categories and their categorical traces
Arnaud Eteve
TL;DR
This paper introduces a new construction for free monodromic categories, simplifies their Hecke categories, and computes their traces, leading to new proofs of important theorems in Deligne--Lusztig theory.
Contribution
It provides a novel formalism for free monodromic categories, simplifying their construction and enabling trace computations, with applications to Deligne--Lusztig theory.
Findings
New construction of free monodromic categories
Simplified constructions of free monodromic Hecke categories
Computed traces of Frobenius and identity on these categories
Abstract
The goal of this paper is to give a new construction of the free monodromic categories defined by Yun. We then use this formalism to give simpler constructions of the free monodromic Hecke categories and then compute the trace of Frobenius and of the identity on them. As a first application of the formalism, we produce new proofs of key theorems in Deligne--Lusztig theory.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology