A reciprocity law and the skew Pieri rule for the symplectic group

We use the theory of skew duality to show that decomposing the tensor product of k irreducible representations of the symplectic group Sp 2m = Sp 2m (C) is equivalent to branching from Sp 2n to Sp 2n1 ..... 2nk , where n, n1, . . . , nk are positive integers such that n = n 1 +. . . . +n k and the njs depend on m as well as the representations in the tensor product. Using this result and a work of Lepowsky, we obtain a skew Pieri rule for Sp 2m , i.e., a description of the irreducible decomposition of the tensor product of an irreducible representation of the symplectic group Sp 2m with a fundamental representation. Published by AIP Publishing.

A reciprocity law and the skew Pieri rule for the symplectic group Academic Article