Branching formula for q-Littlewood–Richardson coefficients

AbstractA generalized inversion statistic is introduced on k-tuples of semistandard tableaux. It is shown that the cospin of a semistandard k-ribbon tableau is equal to the generalized inversion number of its k-quotient. This leads to a branching formula for the q-analogue of Littlewood–Richardson coefficients defined by Lascoux, Leclerc, and Thibon. This branching formula generalizes a recurrence of Garsia and Procesi involving Kostka–Foulkes polynomials