The Howe duality and polynomial solutions for the symplectic Dirac operator
Representation Theory
2016-01-06 v3 Symplectic Geometry
Abstract
We study various aspects of the metaplectic Howe duality realized by Fischer decomposition for the metaplectic representation space of polynomials on 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.
Cite
@article{arxiv.1002.1053,
title = {The Howe duality and polynomial solutions for the symplectic Dirac operator},
author = {Hendrik De Bie and Petr Somberg and Vladimír Souček},
journal= {arXiv preprint arXiv:1002.1053},
year = {2016}
}
Comments
13 pages, to appear in J. Geom. Phys