Metaplectic and spin representations: a parallel treatment

2022/12/09 by Naranjo-Alvarado, Adrián J., Várilly, Joseph C.
#22E70. Secondary 46E20 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 22E46 #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2212.04626

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^c and Spin^c covering groups, acting on the respective Fock spaces by permuting certain Gaussian vectors. The cocycles of these extensions exhibit interesting similarities.

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