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

Olivier Dudas (1, 2) , Alexander B. Ivanov

1 UFR Mathématiques UPCité - UFR Mathématiques [Sciences] - Université Paris Cité
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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).

Domaines: Théorie des représentations [math.RT]

Olivier Dudas, Alexander B. Ivanov. Orthogonality relations for deep level Deligne--Lusztig schemes of Coxeter type. 2021. ⟨hal-03456443⟩