Rocky Mountain Journal of Mathematics

Morita equivalences of spin blocks of symmetric and alternating groups

Ruthi Leabovich and Mary Schaps

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Abstract

We complete the demonstration of source algebra equivalences between spin blocks of families of covering groups $\{\widetilde {S}_n\}$ and $\{\widetilde {A}_n\}$ of symmetric and alternating groups, for pairs of blocks at the ends of maximal strings. These equivalences remain within the family of groups if cores of the two blocks have the same parity and cross over from one family to the other if the cores are of opposite parity. This demonstrates Kessar and Schaps' crossover conjecture for the easier case of extremal points of maximal strings. We use this result to give an improved bound for the highest degree necessary in order to get representatives of all Morita equivalence classes of spin blocks for a given weight.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 3 (2017), 863-904.

Dates
First available in Project Euclid: 24 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1498269815

Digital Object Identifier
doi:10.1216/RMJ-2017-47-3-863

Mathematical Reviews number (MathSciNet)
MR3682153

Zentralblatt MATH identifier
06741624

Subjects
Primary: 20C05: Group rings of finite groups and their modules [See also 16S34] 20C20: Modular representations and characters

Keywords
Donovan's conjecture spin blocks Scopes involution Morita equivalence

Citation

Leabovich, Ruthi; Schaps, Mary. Morita equivalences of spin blocks of symmetric and alternating groups. Rocky Mountain J. Math. 47 (2017), no. 3, 863--904. doi:10.1216/RMJ-2017-47-3-863. https://projecteuclid.org/euclid.rmjm/1498269815


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