2009/07/04 by Mark Wildon, Wildon, Mark · 2 citations
Mathematics · #20C20 #20C30 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20C20 #msc:20C30
paper · pdf · doi:10.48550/arxiv.0907.0811
18 pages, 1 figure
arxiv created 2009/07/04 · openalex publication_date 2009/07/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht module, a large subgroup contained in one of its vertices. A corollary of this theorem is a new way to determine the defect groups of symmetric groups. We also use it to find the Green correspondents of a particular family of simple Specht modules; as a corollary, we get a new proof of the Brauer correspondence for blocks of the symmetric group. The proof of the main theorem uses the Brauer homomorphism on modules, as developed by M. Broué, together with combinatorial arguments using Young tableaux.