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arXiv · 2407.18694

Deep level Deligne--Lusztig representations of Coxeter type

Alexander B. Ivanov·Sian Nie·Panjun Tan
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Abstract

In this article we study the cohomology of deep level Deligne--Lusztig varieties of Coxeter type, attached to a reductive group over a local non-archimedean field, which splits over an unramified extension. This allows to construct some new irreducible representations of parahoric subgroups of $p$-adic groups. Moreover, in the quasi-split case we prove that these compactly induce to finite direct sums of irreducible supercuspidal representations of the $p$-adic group. This extends previous results of \cite{DI}, \cite{CI_loopGLn}.

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BibTeXRIS

Alexander B. Ivanov, Sian Nie, Panjun Tan. 2024-07-26. Deep level Deligne--Lusztig representations of Coxeter type. https://arxiv.org/abs/2407.18694

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