A Branching Law for the Symplectic Groups
نویسنده
چکیده
Branching laws for the irreducible tensor representations of the general linear and orthogonal groups are well-known. Furthermore, these laws have a simple form [1]. In the case of the symplectic groups, however, the branching law becomes more complicated and is expressed in terms of a determinant. We derive this result here bybrute force applied to the Weyl character formulas, though it could also have been obtained from a more sophisticated treatment of representation theory contained in some unpublished work of Kostant.
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