2014/08/20 by Michael Livesey, Livesey, Michael
Mathematics · #20C15 (Primary) #20C30 (Secondary) #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20C15 #msc:20C30
paper · pdf · doi:10.48550/arxiv.1408.4709
44 pages
openalex publication_date 2014/08/20 · arxiv created 2014/11/26 · arxiv updated 2014/11/27 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
O. Brunat and J. Gramain recently proved that any two blocks of double covers of symmetric groups are Broué perfectly isometric provided they have the same weight and sign. They also proved a corresponding statement for double covers of alternating groups and Broué perfect isometries between double covers of symmetric and alternating groups when the blocks have opposite signs. Using both the results and methods of O. Brunat and J. Gramain in this paper we prove that when the weight of a block of a double cover of a symmetric or alternating group is less than p then the block is Broué perfectly isometric to its Brauer correspondent. This means that Broué's perfect isometry conjecture holds for the double covers of the symmetric and alternating groups. We also explicitly construct the characters of these Brauer correspondents which may be of independent interest to the reader.