2003/04/30 by Cédric Bonnafé, Cedric Bonnafe, Bonnafe, Cedric
Mathematics · #20G40 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20G40
paper · pdf · doi:10.48550/arxiv.math/0304500
Part I is a corrected version of math.GR/0111224 (to appear in J. Group theory) : 37 pages Part II : 34 pages
arxiv created 2003/04/30 · openalex publication_date 2003/04/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part, we construct a new isomorphism between the endomorphism algebra of an induced cuspidal character sheaf and the group algebra of the relative Weyl group involved. We show it differs from the isomorphism of Lusztig by a linear character, and we relate this linear character to some stabilizers. Some consequences for characteristic functions of character sheaves are obtained. In the second part, we compute explicitly this linear character whenever the cuspidal local system is supported by the regular unipotent class and, as an application of these methods, we obtain a refinement of Digne, Lehrer and Michel's theorem on Lusztig restriction of Gel'fand-Graev characters.