Special and general types
For a symplectic manifold a metaplectic structure on is a G-structure for the metaplectic group, hence a lift of structure groups of the tangent bundle from the symplectic group to the metaplectic group through the double cover map :
Analogously for the Mp^c-group one considers -structures.
(Bates-Weinstein, theorem 7.16)
Existence of -structures
(Robinson-Rawnsley 89, theorem (6.2))
For more details, see at metaplectic group – (Non-)Triviality of Extensions.
Michael Forger, Harald Hess, Universal metaplectic structures and geometric quantization, Comm. Math. Phys. Volume 64, Number 3 (1979), 269-278. (EUCLID)
R. J. Plymen, The Weyl bundle, Journal of Functional Analysis 49, 186-197 (1982) (journal)
P. L. Robinson, John Rawnsley, The metaplectic representation, -structures and geometric quantization, 1989
Michel Cahen, Simone Gutt, John Rawnsley, Symplectic Dirac Operators and -structures (arXiv:1106.0588)
Sean Bates, Alan Weinstein, Lectures on the geometry of quantization, (pdf)
Revised on January 21, 2015 23:35:06
by Urs Schreiber