On a multiplicity formula of weights of representations of 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 to the frequency of occurrence of an irreducible holomorphically induced representation of the group in an *n*-fold tensor product of irreducible symmetric representations of is given. Reciprocity theorems relating holomorphic discrete series of (resp. ) to holomorphically induced representations of (resp. ) are also derived.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1227520-2

Keywords:
Weights of representations,
reciprocity theorems,
holomorphic discrete series,
holomorphically induced representations,
dual pairs

Article copyright:
© Copyright 1995
American Mathematical Society