Modular spin representations of the symmetric group

Abstract

1. Let Γn be the representation group or spin group (4, 9) of Sn. Then the irreducible representations of Γn are of two distinct types. These are (a) ordinary representations, which are the irreducible representations of the symmetric group and (b) spin or projective representations. Corresponding to every partition (λ) = (λ1, λ2, …, λm) of n with λ1 > λ2 > … > λm > 0 there is an irreducible spin representation 〈λ〉 of Γn.