Metaplectic and spin representations: a parallel treatment

arXiv2212.04626MaRDI QIDQ6420030

Adrián J. Naranjo-Alvarado, Joseph C. Várilly

Publication date: 8 December 2022

Abstract: The analogies between symplectic and orthogonal groups, regarded as symmetries of real bilinear forms, are manifest in their (metaplectic and spin) projective representations. In finite dimensions, those are true representations of doubly covering groups; but one may also use group extensions by a circle. Here we lay out a parallel treatment of of the Mp$m^{}athrmc$ and Spin$m^{}athrmc$ covering groups, acting on the respective Fock spaces by permuting certain Gaussian vectors. The cocycles of these extensions exhibit interesting similarities.

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Semisimple Lie groups and their representations (22E46) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

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