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Open problems on Iwahori-Hecke algebras

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arxiv 2006.08535 v1 pith:RACELVRJ submitted 2020-06-15 math.RT

G. Lusztig This is my paper · ORCID
classification math.RT
keywords algebrasappearingconjectureheckeiwahori-heckeopenproblemssome
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We state four open problems on Iwahori-Hecke algebras. The first one states a relation between some algebras appearing in Solleveld's work and some explicit Hecke algebras appearing in the study of unipotent representations. The second one is a boundedness conjecture. The third one is a conjecture of well-definedness of an asymptotic Hecke algebra. The fourth one concerns positive conjugacy classes in a Weyl group.

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  1. On parameters of Hecke algebras for $p$-adic groups

    math.RT 2025-05 accept novelty 7.0 of 10

    Depth-zero Hecke algebra parameters equal unipotent Hecke algebra parameters, proving a version of Lusztig's conjecture under tameness.

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