5 papers
On the Schematic and Analytic Constructions of the Local Langlands Category
Ian Gleason, Linus Hamann, Alexander B. Ivanov +2
We prove a folklore conjecture identifying two categorical enhancements of the automorphic side of the local Langlands correspondence. Concretely, we construct an equivalence for t…
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…
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…
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…