Decomposition numbers for abelian defect RoCK blocks of double covers of symmetric groups

verfasst von

Matthew Fayers, Alexander Kleshchev, Lucia Morotti

Abstract

We calculate the (super)decomposition matrix for a RoCK block of a double cover of the symmetric group with abelian defect, verifying a conjecture of the first author. To do this, we exploit a theorem of the second author and Livesey that a RoCK block (Formula presented.) is Morita superequivalent to a wreath superproduct of a certain quiver (super)algebra with the symmetric group (Formula presented.). We develop the representation theory of this wreath superproduct to compute its Cartan invariants. We then directly construct projective characters for (Formula presented.) to calculate its decomposition matrix up to a triangular adjustment, and show that this adjustment is trivial by comparing Cartan invariants.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Queen Mary University of London
University of Oregon

Typ

Artikel

Journal

Journal of the London Mathematical Society

Band

109

Anzahl der Seiten

49

ISSN

0024-6107

Publikationsdatum

31.01.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://doi.org/10.1112/jlms.12852 (Zugang: Offen)