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Geometric quantization with metaplectic-c structures

Banff International Research Station for Mathematical Innovation and Discovery

In the classical geometric quantization procedure with the "half-form correction", one cannot quantize a complex projective space of even complex dimension (there is no "half form bundle"), and one cannot equivariantly quantize any symplectic toric manifold (there is no "equivariant half form bundle"). I will describe a geometric quantization procedure that uses metaplectic-c structures to incorporate the "half form correction" into the prequantization stage and that does apply to these examples. This follows work of Harald Hess from the late 1970s, with recent contributions of Jennifer Vaughan.

Mathematics; Differential geometry; Topological groups, lie groups

video/mp4

Author affiliation: University of Toronto

2019-03-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69281

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/