The Howe duality and polynomial solutions for the symplectic Dirac operator
De Bie, Hendrik · Somberg, Petr · Souček, Vladimír
Original · EN
We study various aspects of the metaplectic Howe duality realized by Fischer decomposition for the metaplectic representation space of polynomials on R²ⁿ 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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