Generalized Green functions and unipotent classes for finite reductive groups, IV

2024/08/30 by Frank Lübeck, Lübeck, Frank, Toshiaki Shoji +1
Mathematics · #20G05 #20G40 #Advanced Algebra and Geometry #Advanced Mathematical Identities #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2408.16960

openalex publication_date 2024/08/30 · openalex created_date 2024/09/29 · openalex updated_date 2026/07/28

Abstract

In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group G. Generalized Green functions of G can be computed by using Lusztig's algorithm, if split elements exist for any unipotent class. The existence of split elements is reduced to the case where G is a simply connected, almost simple group. We show, in the case of classical groups, split elements exist, which is a refinement of previous results. In the case of exceptional groups, we show the existence of split elements, possibly except one class for G of type E₇.

Related

• Generalized Green functions and unipotent classes for finite reductive groups, II
• Generalized Green functions and unipotent classes for finite reductive groups, III
• Generalized Green functions and unipotent classes for finite reductive groups, I
• Remarks on computing Green functions
• The space of unipotently supported class functions on a finite reductive group