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).