Cohomology of symplectic spinor twisted de Rham sequence and its subcomplexes
Svatopluk Kryls (Mathematical Institute, Charles University)
Abstract: Symplectic spinors were discovered by Segal and Shale in 1962 in the realm of quantum physics and by Weil in 1964 in the realm of analysis on p-adic groups and number theory. They were incorporated into global analysis and geometry some decades after that.
We treat a sheaf resolution of symplectic spinors and a sheaf sub-resolution induced by symplectic connections and by symplectic Ricci-type connections, respectively. The latter named connections (also called symplectic Weyl-flat and symplectic curvature reducible) were investigated in differential geometry a) as parallel notions to Weyl- and Ricci-type connections known in the Riemannian case, and also b) for the aims of geometric quantization.
We introduce the resolutions and induced complexes, using a modest amount of representation theory. Besides giving theorems on them, we mention their Riemannian counterparts regarding their existence.
mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory
Audience: researchers in the topic
Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics
Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.
| Organizers: | Hong Van Le*, Igor Khavkine*, Anton Galaev, Alexei Kotov, Petr Somberg, Roman Golovko |
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