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arXiv · 1002.1053

The Howe duality and polynomial solutions for the symplectic Dirac operator

Hendrik De Bie·Petr Somberg·Vladimír Souček
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Abstract

We study various aspects of the metaplectic Howe duality realized by Fischer decomposition for the metaplectic representation space of polynomials on $\mathbb{R}^{2n}$ valued in the Segal-Shale-Weil representation. As a consequence, we determine symplectic monogenics, i.e., the space of polynomial solutions of the symplectic Dirac operator.

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Hendrik De Bie, Petr Somberg, Vladimír Souček. 2010-02-04. The Howe duality and polynomial solutions for the symplectic Dirac operator. https://arxiv.org/abs/1002.1053

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