Signed Young Modules and Simple Specht Modules

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Danz, Susanne; Lim, Kay Jin; (2015)
  • Subject: Mathematics - Representation Theory
    arxiv: Mathematics::Representation Theory | Astrophysics::Galaxy Astrophysics

By a result of Hemmer, every simple Specht module of a finite symmetric group over a field of odd characteristic is a signed Young module. While Specht modules are parametrized by partitions, indecomposable signed Young modules are parametrized by certain pairs of parti... View more
  • References (24)
    24 references, page 1 of 3

    2.7. Young subgroups, wreath products, Sylow p-subgroups of Sn. Let n ∈ Z+ . (a) For a partition, or, more generally, a composition λ = (λ1, . . . , λk) of n, we denote by Sλ = Sλ1 × · · · × Sλk the corresponding standard Young subgroup of Sn. (b) Let G be any finite group, and let H 6 Sn. We have the wreath product G ≀ H := {(g1, . . . , gn; σ) : g1, . . . , gn ∈ G, σ ∈ H}, whose multiplication is given by the trivial F Sα-module F (α) to Sk ≀ Sα. Moreover, if k is odd then s\gn(k) s\gn(k)⊗βt ∼= sgn(Sk ≀ Sβ) (see Remark 3.11). Now set [2] M. Broué, On Scott modules and p-permutation modules: an approach through the Brauer morphism, Proc. Amer. Math. Soc. 93 (1985), no. 3, 401-408.

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