A new proof of a theorem of Littlewood

In this paper we give a new combinatorial proof of a result of Littlewood [D.E. Littlewood, The Theory of Group Characters, 2nd ed., Oxford University Press, 1950], p. 124: Sμ(1,q,q2,…)=qn(μ)∏s∈μ(1−qhμ(s)), where Sμ denotes the Schur function of the partition μ, n(μ) is the sum of the legs of the cells of μ and hμ(s) is the hook number of the cell s∈μ.