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Deep level Deligne--Lusztig representations of Coxeter type

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arxiv 2407.18694 v2 pith:ZUXCMGKK submitted 2024-07-26 math.RT math.AG

Alexander B. Ivanov , Sian Nie , Panjun Tan This is my paper
classification math.RTmath.AG
keywords representationsadiccitecoxeterdeepdeligne--lusztiggroupirreducible
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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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  1. Green functions for positive-depth Deligne--Lusztig induction

    math.RT 2025-06 accept novelty 7.0 of 10

    For large q, positive-depth Deligne-Lusztig induction matches the Yu-Kaletha-FKS algebraic construction for all Howe-unramified elliptic pairs, via a characterization theorem and a Green function comparison.

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