On the Formal Degree Conjecture for Non-Singular Supercuspidal Representations

DOI10.1093/IMRN/RNAC154arXiv2106.00878OpenAlexW4302311766WikidataQ113819034 ScholiaQ113819034MaRDI QIDQ6115183

Kazuma Ohara

Publication date: 12 July 2023

Published in: Unnamed Author (Search for Journal in Brave)

Abstract: We prove the formal degree conjecture for non-singular supercuspidal representations based on Schwein's work proving the formal degree conjecture for regular supercuspidal representations. The main difference between our work and Schwein's work is that in non-singular case, the Deligne--Lusztig representations can be reducible, and the $S$-groups are not necessary abelian. Therefore, we have to compare the dimensions of irreducible constituents of the Deligne--Lusztig representations and the dimensions of irreducible representations of $S$-groups.

Full work available at URL: https://arxiv.org/abs/2106.00878

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

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Simple supercuspidals and the Langlands correspondence

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