A combinatorial approach to Specht module cohomology

Details A combinatorial approach to Specht module cohomology A combinatorial approach to Specht module cohomology

2009-10-27

arxiv.org/abs/0910.5229v1

Mathematics

Representation Theory

Scientific paper

For a Specht module S^\lambda for the symmetric group \Sigma_d, the cohomology H^i(\Sigma_d, S^\lambda) is known only in degree i=0. We give a combinatorial criterion equivalent to the nonvanishing of the degree i=1 cohomology, valid in odd characteristic. Our condition generalizes James' solution in degree zero. We apply this combinatorial description to give some computations of Specht module cohomology, together with an explicit description of the corresponding modules. Finally we suggest some general conjectures that might be particularly amenable to proof using this description.

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