Cohomology and generic cohomology of Specht modules for the symmetric group

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dc.creatorHemmer, David J.
dc.date2008-03-26
dc.date2009-01-28
dc.date.accessioned2026-07-07T12:34:41Z
dc.date.available2026-07-07T12:34:41Z
dc.descriptionCohomology of Specht modules for the symmetric group can be equated in low degrees with corresponding cohomology for the Borel subgroup B of the general linear group GL_d(k), but this has never been exploited to prove new symmetric group results. Using work of Doty on the submodule structure of symmetric powers of the natural GL_d(k) module together with work of Andersen on cohomology for B and its Frobenius kernels, we prove new results about H^i(Σ_d, S^λ). We recover work of James in the case i=0. Then we prove two stability theorems, one of which is a "generic cohomology" result for Specht modules equating cohomology of S^{pλ} with S^{p^2λ}. This is the first theorem we know relating Specht modules S^λand S^{pλ}. The second result equates cohomology of S^λwith S^{λ+ p^aμ} for large a.
dc.descriptionSome substantial revisions from previous version
dc.identifierhttps://arxiv.org/abs/0803.3764
dc.identifierhttp://arxiv.org/abs/0803.3764
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217522
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject20C30; 20G10
dc.titleCohomology and generic cohomology of Specht modules for the symmetric group
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