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math.RT2024
Convex elements and Steinberg's cross-sections
Sian Nie, Panjun Tan, Qingchao Yu
In this paper, we study convex elements in a (twisted) Weyl group introduced by Ivanov and the first named author. We show that each conjugacy class of the twisted Weyl group conta…
math.RT2024
Deep level Deligne--Lusztig representations of Coxeter type
Alexander B. Ivanov, Sian Nie, Panjun Tan
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 ove…
math.RT2024
Decomposition of higher Deligne-Lusztig representations
Sian Nie
Higher Deligne-Lusztig representations are virtual smooth representations of parahoric subgroups in a -adic group. They are natural analogs of classical Deligne-Lusztig represen…