Published online by Cambridge University Press: 06 March 2002
This paper deals with some character values of the symmetric group Sn as well as its double cover S˜n.
Let χλ(ρ) be the irreducible character of Sn, indexed by the partition λ and evaluated at the conjugacy class ρ. Comparing the character tables of S2 and S4, one observes that
for ρ = (2), 2ρ = (4) and ρ = (12), 2ρ = (22). A number of such observations lead to what we call Littlewood's multiple formula (Theorem 1.1). This formula appears in Littlewood's book [2]. We include a proof that is based on an ‘inflation’ of the variables in a Schur function. This is different from one given in [2], and we claim that it is more complete than the one given there.
Our main objective is to obtain the spin character version of Littlewood's multiple formula (Theorem 2.3).