9 papers
Symmetric spaces over a finite ring
Ben Liu, Sian Nie
Deep level Deligne-Lusztig representations, as natural extensions of the classical Deligne-Lusztig representations, have recently seen various applications in the Langlands program…
Deep level Deligne--Lusztig induction for tamely ramified tori
Alexander B. Ivanov, Sian Nie
Deep level Deligne--Lusztig representations, which are natural analogues of classical Deligne--Lusztig representations, recently play an important role in geometrization of irreduc…
An alternative construction of character sheaves on parahoric subgroups
Alexander B. Ivanov, Sian Nie, Zhihang Yu
Inspired by the foundational work of Bezrukavnikov and Chan \cite{BC24} on character sheaves for parahoric subgroups and an alternative interpretation of deep level Deligne-Lusztig…
Lifting Deligne-Lusztig Reduction and Geometric Coxeter Type Elements
Sian Nie, Felix Schremmer, Qingchao Yu
Cases of Shimura varieties where the special fibre of a Rapoport-Zink space is simply the union of classical Deligne-Lusztig varieties are known as fully Hodge-Newton decomposable…
An explicit decomposition of higher Deligne-Lsuztig representations
Ben Liu, Sian Nie
In a previous paper, the second named author obtains a decomposition of an elliptic higher Deligne-Lusztig representation into irreducible summands, which are built in the same way…
Convex elements and cohomology of deep level Deligne-Lusztig varieties
Alexander B. Ivanov, Sian Nie
We essentially complete a program initiated by Boyarchenko--Weinstein to give a full description of the cohomology of deep level Deligne--Lusztig varieties for elliptic tori, with…
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…
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…
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…