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Spin modules for symmetric groups. (English) Zbl 0669.20005
The 2-modular irreducible representations \(D^\lambda\) of the symmetric group \(\Sigma_n\) are indexed canonically by the partitions \(\lambda\) of \(n\) into distinct parts. Theorem 1 of the paper gives an explicit description of those \(\lambda\) for which the restriction of \(D^\lambda\) to the alternating group splits as a sum of two non-isomorphic irreducible modules. Theorem 2 describes the possible decomposition factors of the reduction modulo 2 of some spin representations for \(\Sigma_n\). The formulation depends on a doubling operator on partitions. The author remarks that the ideas of the paper go some way towards constructing analogues for the Specht modules, for the spin representations.
Reviewer: J.B.Olsson

MSC:
20C30 Representations of finite symmetric groups
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