# zbMATH — the first resource for mathematics

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
Full Text: