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The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator. (English) Zbl 1279.30051
Summary: We study various aspects of the metaplectic Howe duality realized by the 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 \(D_s\).

30G35 Functions of hypercomplex variables and generalized variables
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
Full Text: DOI
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