Decomposition of a tensor product of a higher symplectic spinor module and the defining representation of sp(2n,C)

摘要

Let L(lambda) be the irreducible highest weight sp(2n,C)-module with a highest weight lambda, such that L(lambda) is an infinite dimensional module with bounded multiplicities, and let F((w) over bar (1)) be the defining representation of sp (2n, C). In this article, the tensor product L(lambda) circle times F((w) over bar (1)) is explicitly decomposed into irreducible summands. This decomposition may be used in order to define some invariant first order differential operators for metaplectic structures.