2019/10/09 by Junbin Dong, Yang Gao, Dong, Junbin +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1910.03764
openalex publication_date 2019/10/09 · openalex created_date 2019/10/18 · openalex updated_date 2026/07/28
For a connected reductive algebraic group G defined over a finite field \mathbb Fq, Kawanaka introduced the generalized Gelfand-Graev representations (GGGRs for short) of the finite group G(\mathbb Fq) in the case where q is a power of a good prime for G. This representation has been widely studied and used in various contexts. Recently, Geck proposed a conjecture, characterizing Lusztig's special unipotent classes in terms of weighted Dynkin diagrams. Based on this conjecture, he gave a guideline for extending the definition of GGGRs to the case where q is a power of a bad prime for G. Here, we will give a proof of Geck's conjecture. Combined with Geck's pioneer work, our proof verifies Geck's conjectural characterization of special unipotent classes, and completes his definition of GGGRs in bad characteristics.