Irreducible Specht modules are signed Young modules

Article, Preprint English OPEN
Hemmer, David J. (2005)
  • Publisher: Elsevier BV
  • Journal: Journal of Algebra, volume 305, issue 1, pages 433-441 (issn: 0021-8693)
  • Related identifiers: doi: 10.1016/j.jalgebra.2006.01.046
  • Subject: 20C30 | Algebra and Number Theory | Mathematics - Representation Theory
    arxiv: Mathematics::Representation Theory | Astrophysics::Galaxy Astrophysics | Astrophysics::Solar and Stellar Astrophysics

Recently Donkin defined signed Young modules as a simultaneous generalization of Young and twisted Young modules for the symmetric group. We show that in odd characteristic, if a Specht module $S^\lambda$ is irreducible, then $S^\lambda$ is a signed Young module. Thus the set of irreducible Specht modules coincides with the set of irreducible signed Young modules. This provides evidence for our conjecture that the signed Young modules are precisely the class of indecomposable self-dual modules with Specht filtrations. The theorem is false in characteristic two.
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