Principal covariants, multiplicity-free actions, and the K-types of holomorphic series

Howe, Roger and Kraft, Hanspeter. (1997) Principal covariants, multiplicity-free actions, and the K-types of holomorphic series. Progress in mathematics, 158. pp. 147-161.

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Official URL: http://edoc.unibas.ch/dok/A5842780

We prove a result on the structure of the $K$-types for holomorphic discrete series of $Sp(2n,R)$. The proof applies the theory of multiplicity-free actions to the realization of holomorphic discrete series by means of the dual pair $(Sp_{2n}, O_m)$.