First degree cohomology of Specht modules and extensions of symmetric powers
Advances in Mathematics(2019)
Abstract
Let Σd denote the symmetric group of degree d and let K be a field of positive characteristic p. For p>2 we give an explicit description of the first cohomology group H1(Σd,Sp(λ)), of the Specht module Sp(λ) over K, labelled by a partition λ of d.
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Key words
Symmetric groups,Cohomology,Specht modules,General linear groups,Extensions,Induced modules
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