Low-degree Cohomology of Integral Specht Modules

Details Low-degree Cohomology of Integral Specht Modules Low-degree Cohomology of Integral Specht Modules

2009-05-26

arxiv.org/abs/0905.4209v1

Experimental Mathematics 18 (2009), no. 1, 85-95

Mathematics

Group Theory

25 pages

Scientific paper

We introduce a way of describing cohomology of the symmetric groups with coefficients in Specht modules over Z or F_p. We study i-th-degree cohomology for i in {0,1,2}. The focus lies on the isomorphism type of second-degree cohomology of integral Specht modules. Unfortunately, only in few cases can we determine this exactly. In many cases we obtain only some information about the prime divisors of the cohomology group's order. The most important tools we use are the Zassenhaus algorithm, the Branching Rules, Bockstein type homomorphisms, and the results from [Burichenko et al., 1996].

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