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 \(D_s\).
MSC:
| 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) |
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