Cuspidal ℓ -modular representations of p-adic classical groups

Rob Kurinczuk, Shaun Stevens

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Abstract

For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced from a cuspidal type. We also give a fundamental step towards the classification of cuspidal representations, identifying when certain cuspidal types induce to equivalent representations; this result is new even in the case of complex representations. Finally, we prove that the representations induced from more general types are quasi-projective, a crucial tool for extending the results here to arbitrary irreducible representations.
Original languageEnglish
Pages (from-to)23–69
Number of pages47
JournalJournal für die reine und angewandte Mathematik (Crelles Journal)
Volume2020
Issue number764
Early online date7 May 2019
DOIs
Publication statusPublished - 1 Jul 2020

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