RoCK blocks of double covers of symmetric groups and generalized Schur algebras

2024/11/06 by Alexander Kleshchev, Kleshchev, Alexander
Engineering · Mathematics · #20C20 #20C30 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2411.03653

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study blocks of the double covers of symmetric and alternating groups. The main result is a `local' description, up to Morita equivalence, of arbitrary defect RoCK blocks of these groups in terms of generalized Schur superalgebras corresponding to an explicit Brauer tree superalgebra. In view of the recent results on Broué's Conjecture for these groups, our result provides a `local' description of an arbitrary block of the double covers of symmetric and alternating groups up to derived equivalence.

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