Address:
M. Holíková, Department of Mathematics and Mathematical Education, Faculty of Education,Charles University, Magdalény Rettigové 4, 116 39 Praha 1, Czech Republic
L. Křižka, Mathematical Institute of Charles University, Sokolovská 83, 180 00 Praha 8, Czech Republic
P. Somberg, Mathematical Institute of Charles University, Sokolovská 83, 180 00 Praha 8, Czech Republic
E-mail:
marie.holikova@pedf.cuni.cz
krizka@karlin.mff.cuni.cz
somberg@karlin.mff.cuni.cz
Abstract: Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective geometry in two real dimensions is ${\widetilde{}}(3,)$.
AMSclassification: primary 53C30; secondary 53D05, 81R25.
Keywords: projective structure, Segal-Shale-Weil representation, generalized Verma modules, symplectic Dirac operator, (3,).
DOI: 10.5817/AM2016-5-313