Spin modules for symmetric groups. (English) Zbl 0669.20005

Benson, Dave

J. Lond. Math. Soc., II. Ser. 38, No. 2, 250-262 (1988).

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

Keywords:

2-modular irreducible representations; symmetric groups; alternating groups; irreducible modules; decomposition factors; spin representations; partitions; Specht modules