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arXiv · 1912.07851

Local Langlands correspondence for regular supercuspidal representations of GL(n)

Masao Oi·Kazuki Tokimoto
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Abstract

In this paper, we prove the coincidence of Kaletha's recent construction of the local Langlands correspondence for regular supercuspidal representations with Harris--Taylor's one in the case of general linear groups. The keys are Bushnell--Henniart's essentially tame local Langlands correspondence and Tam's result on Bushnell--Henniart's rectifiers. By combining them, our problem is reduced to an elementary root-theoretic computation on the difference between Kaletha's and Tam's $χ$-data.

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Masao Oi, Kazuki Tokimoto. 2020-05-30. Local Langlands correspondence for regular supercuspidal representations of GL(n). https://arxiv.org/abs/1912.07851

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