Geodesic
A Note on Howe Duality Correspondence and Isotropy Representations for Unitary Lowest Weight Modules of Mp(n,R)
Journal of Lie theory, Tome 19 (2009) no. 4, pp. 671-683.

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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.
Classification : 17B10, 22E45, 22E46
Mots-clés : 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},
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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, Tome 19 (2009) no. 4, pp. 671-683. http://geodesic.mathdoc.fr/item/JLT_2009_19_4_JLT_2009_19_4_a2/