On the inner products of some Deligne--Lusztig type representations

2017/11/28 by Zhe Chen, Chen, Zhe
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1711.10208

openalex publication_date 2017/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a family of Deligne--Lusztig type varieties attached to connected reductive groups over quotients of discrete valuation rings, naturally generalising the higher Deligne--Lusztig varieties and some constructions related to the algebraisation problem raised by Lusztig. We establish the inner product formula between the representations associated to these varieties and the higher Deligne--Lusztig representations.

Related

• The algebraisation of higher Deligne--Lusztig representations
• The algebraisation of higher level Deligne--Lusztig representations II: odd levels
• Representations of reductive groups over finite rings and extended Deligne-Lusztig varieties
• Representations of Reductive Groups over Quotients of Local Rings
• Flags and orbits of connected reductive groups over local rings