Rocky Mountain Journal of Mathematics

Morita equivalences of spin blocks of symmetric and alternating groups

Ruthi Leabovich and Mary Schaps

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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

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

First available in Project Euclid: 24 June 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Donovan's conjecture spin blocks Scopes involution Morita equivalence


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.

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