A Family of Z Bases for the Ring of Sn Characters and Applications to the Decomposition of Kronecker Products

AbstractWe introduce a new family of Z bases for the ring of Sn characters and give their transition matrices explicitly. Applying one of these bases, we introduce a recursive formula for the Kronecker product of two characters. Another application is a sufficient condition for the vanishing of the coefficient of an irreducible character in a Kronecker product