
Journal of Lie Theory 19 (2009), No. 4, 671683 Copyright Heldermann Verlag 2009 A Note on Howe Duality Correspondence and Isotropy Representations for Unitary Lowest Weight Modules of Mp(n,R) Noriyuki Abe Graduate School of Mathematical Sciences, University of Tokyo, 381 Komaba, Meguroku, Tokyo 1538914, Japan abenori@ms.utokyo.ac.jp Hiroshi Yamashita Department of Mathematics, Faculty of Science, Hokkaido University, N10 W8 Kitaku, Sapporo 0600810, Japan yamasita@math.sci.hokudai.ac.jp [Abstractpdf] 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. Keywords: Metaplectic group, lowest weight module, Howe duality theorem, branching rule, Harish Chandra modules. MSC: 17B10, 22E45, 22E46 [ Fulltextpdf (225 KB)] for subscribers only. 