The Howe duality and polynomial solutions for the symplectic Dirac operator

Details The Howe duality and polynomial solutions for the symplectic Dirac operator The Howe duality and polynomial solutions for the symplectic Dirac operator

2010-02-04

arxiv.org/abs/1002.1053v1

Mathematics

Representation Theory

11 pages

Scientific paper

We find the Fisher decomposition for the space of polynomials valued in the
Segal-Shale-Weil representation. As a consequence, this allows to determine
symplectic monogenics, i.e. the space of polynomial solutions of the symplectic
Dirac operator.

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