A Littlewood–Richardson rule for the Macdonald inner product and bimodules over wreath products

We prove a Littlewood–Richardson type formula for (sλ/μ,sν/κ)tk,t(sλ/μ,sν/κ)tk,t, the pairing of two skew Schur functions in the Macdonald inner product at q=tkq=tk for positive integers k  . This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra C[x]/xkC[x]/xk and symmetric groups.