The varieties for some Specht modules

Details The varieties for some Specht modules The varieties for some Specht modules

2009-03-02

arxiv.org/abs/0903.0409v1

J. Algebra 321 (2009), no. 8, 2287-2301

Mathematics

Representation Theory

to appear in Journal of Algebra

Scientific paper

We concern the VIGRE's conjecture; namely the complexity of a Specht module is the p-weight of the corresponding partition if and only if the partition is not p by p. In abelian defect case, we calculate the cohomological variety of the Specht modules. In particular, we show that the Specht modules have complexities exactly given by the p-weights of the corresponding partitions. For some p-regular partitions not more than p parts with empty p-core, we show that the Specht modules fit into the conjecture. For the partition p^p, we show that the Specht module has complexity p-1 and we study the rank variety of the Specht module restricted to a maximal elementary abelian p-subgroup of rank p.

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