A Note on Howe Duality Correspondence and Isotropy Representations for Unitary Lowest Weight Modules of Mp(n,R)

N. Abe; H. Yamashita

doi:10.5802/jolt.574

N. Abe; H. Yamashita

Journal of Lie Theory, Volume 19 (2009) no. 4, pp. 671-683

Abstract

We give a new proof of the Howe duality theorem for the reductive dual pair $({\rm Sp}(n,\mathbb{R}), {\rm O}(k))$ by using the isotropy representations for unitary lowest weight modules of the metaplectic group ${\rm Mp}(n,\mathbb{R})$. The irreducible representations of $O(k)$ appearing in the Howe duality correspondence are specified explicitly by means of the branching rule of the representations of O$(k)$ restricted to orthogonal groups of smaller size.

Zbl

DOI: 10.5802/jolt.574

Classification: 17B10, 22E45, 22E46
Keywords: Metaplectic group, lowest weight module, Howe duality theorem, branching rule, Harish Chandra modules

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     author = {N. Abe and H. Yamashita},
     title = {A {Note} on {Howe} {Duality} {Correspondence} and {Isotropy} {Representations} for {Unitary} {Lowest} {Weight} {Modules} of {Mp(n,R)}},
     journal = {Journal of Lie Theory},
     pages = {671--683},
     year = {2009},
     volume = {19},
     number = {4},
     doi = {10.5802/jolt.574},
     zbl = {1242.22018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.574/}
}

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N. Abe; H. Yamashita. A Note on Howe Duality Correspondence and Isotropy Representations for Unitary Lowest Weight Modules of Mp(n,R). Journal of Lie Theory, Volume 19 (2009) no. 4, pp. 671-683. doi: 10.5802/jolt.574

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