Geodesic
Projective structure, $\widetilde{\operatorname{SL}}(3,\mathbb{R})$ and the symplectic Dirac operator
Archivum mathematicum, Tome 52 (2016) no. 5, pp. 313-324.

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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 ${\widetilde{}}(3,)$.
DOI : 10.5817/AM2016-5-313
Classification : 53C30, 53D05, 81R25
Keywords: projective structure; Segal-Shale-Weil representation; generalized Verma modules; symplectic Dirac operator; $(3, )$ 
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     title = {Projective structure, $\widetilde{\operatorname{SL}}(3,\mathbb{R})$ and the symplectic {Dirac} operator},
     journal = {Archivum mathematicum},
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Holíková, Marie; Křižka, Libor; Somberg, Petr. Projective structure, $\widetilde{\operatorname{SL}}(3,\mathbb{R})$ and the symplectic Dirac operator. Archivum mathematicum, Tome 52 (2016) no. 5, pp. 313-324. doi : 10.5817/AM2016-5-313. http://geodesic.mathdoc.fr/articles/10.5817/AM2016-5-313/

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