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2009 Low-Degree Cohomology of Integral Specht Modules
Christian Weber
Experiment. Math. 18(1): 85-96 (2009).

Abstract

We introduce a way of describing cohomology of the symmetric groups $\Sig n$ with coefficients in Specht modules. We study $\HlR i$ for $i \in \{0,1,2\}$ and $R = \Z$, $\Fp$. The focus lies on the isomorphism type of $\Hlz 2$. Unfortunately, only in few cases can we determine this exactly. In many cases we obtain only some information about the prime divisors of $|\Hlz 2|$. The most important tools we use are the Zassenhaus algorithm, the branching rules, Bockstein-type homomorphisms, and the results from Burichenko et al., 1996.

Citation

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Christian Weber. "Low-Degree Cohomology of Integral Specht Modules." Experiment. Math. 18 (1) 85 - 96, 2009.

Information

Published: 2009
First available in Project Euclid: 27 May 2009

zbMATH: 1169.20026
MathSciNet: MR2548989

Subjects:
Primary: 20C10 , 20C30 , 20J06

Keywords: Bockstein homomorphism , Cohomology , Specht module , symmetric groups , Zassenhaus algorithm

Rights: Copyright © 2009 A K Peters, Ltd.

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Vol.18 • No. 1 • 2009
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