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On a multiplicity formula of weights of representations of $ {\rm SO}\sp *(2n)$ and reciprocity theorems for symplectic groups

Authors: Eric Y. Leung and Tuong Ton-That
Journal: Proc. Amer. Math. Soc. 123 (1995), 1281-1288
MSC: Primary 22E46; Secondary 22E45
MathSciNet review: 1227520
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Abstract: A formula relating the multiplicity of a weight of a holomorphic discrete series of the group $ S{O^ \ast }(2n)$ to the frequency of occurrence of an irreducible holomorphically induced representation of the group $ Sp(2n,\mathbb{C})$ in an n-fold tensor product of irreducible symmetric representations of $ Sp(2n,\mathbb{C})$ is given. Reciprocity theorems relating holomorphic discrete series of $ S{O^ \ast }(2n)$ (resp. $ Sp(2n,\mathbb{R})$) to holomorphically induced representations of $ Sp(2k,\mathbb{C})$ (resp. $ SO(N,\mathbb{C})$) are also derived.

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Keywords: Weights of representations, reciprocity theorems, holomorphic discrete series, holomorphically induced representations, dual pairs
Article copyright: © Copyright 1995 American Mathematical Society