Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 22 (2012), No. 4, 1049--1063Copyright Heldermann Verlag 2012 Howe Duality for the Metaplectic Group Acting on Symplectic Spinor Valued Forms Svatopluk Krýsl Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8 - Karlín 186 75, Czechia Svatopluk.Krysl@mff.cuni.cz [Abstract-pdf] \def\g{{\frak g}} \def\o{{\frak o}} \def\p{{\frak p}} \def\s{{\frak s}} \def\C{{\Bbb C}} \def\SS{{\Bbb S}} \def\V{{\Bbb V}} \def\W{{\Bbb W}} Let $\SS$ denote the oscillatory module over the complex symplectic Lie algebra $\g= \s\p(\V^\C,\omega)$. Consider the $\g$-module $\W=\bigwedge^{\bullet}(\V^*)^\C\otimes\SS$ of forms with values in the oscillatory module. We prove that the associative commutant algebra $\hbox{\rm End}_\g(\W)$ is generated by the image of a certain representation of the ortho-symplectic Lie super algebra $\o\s\p(1|2)$ and two distinguished projection operators. The space $\W$ is then decomposed with respect to the joint action of $\g$ and $\o\s\p(1|2)$. This establishes a Howe type duality for $\s\p(\V^\C,\omega)$ acting on $\W$. Keywords: Howe duality, symplectic spinors, Segal-Shale-Weil representation, Kostant spinor. MSC: 17B10, 17B45, 22E46, 81R05 [ Fulltext-pdf  (362  KB)] for subscribers only.