Orthogonality relations for deep level Deligne--Lusztig schemes of Coxeter type

Abstract

In this paper we prove some orthogonality relations for representations arising from deep level Deligne--Lusztig schemes of Coxeter type. This generalizes previous results of Lusztig (2004), and of Chan and the second author (2019). Potential applications include the study of unipotent representations arising from such deep level Deligne--Lusztig schemes, as well as their geometry, in the spirit of the work of Lusztig (1976).

22 pages

References in corpus (3)

• Deligne-Lusztig constructions for unipotent and p-adic groups
• On loop Deligne--Lusztig varieties of Coxeter-type for inner forms of ${\mathrm{GL}}_n$
• Cohomological representations of parahoric subgroups

Cited by in corpus (1)

• On a decomposition of $p$-adic Coxeter orbits