Crossover Morita equivalences of spin representations of the symmetric and alternating groups

Details Crossover Morita equivalences of spin representations of the symmetric and alternating groups Crossover Morita equivalences of spin representations of the symmetric and alternating groups

2009-10-27

arxiv.org/abs/0910.5070v1

Mathematics

Representation Theory

Scientific paper

We prove the existence of Morita equivalences between the spin blocks at the extremal points of strings in the block-reduced crystal graph. When the parities of the core partitions are not preserved, these equivalences require crossovers, with a block of the symmtric group Morita equivalent to a block of the alternating group and vice versa. The result permits in improvement of the bound for Donovan's Conjecture given by Kessar.

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