Publication at Faculty of Mathematics and Physics |
2017
Abstract
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(2n_1) x . . . x Sp(2n_k) , where n, n_1, . . . , n_k are positive integers such that n = n_1 + . . . + n_k and the n_j's 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.