Positive definite superfunctions and unitary representations of Lie supergroups

2012/08/13 by Neeb, Karl-Hermann, Salmasian, Hadi
#17B65 #22E45 #22E65 #58C50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1208.2641

Abstract

For a broad class of Frechet-Lie supergroups we prove that there exists a correspondence between positive definite smooth superfunctions and matrix coefficients of unitary representations. We also give a characterization of linear functionals on the corresponding universal enveloping algebra which correspond to matrix coefficients of analytic unitary representations.

Related

• Lie supergroups, unitary representations, and invariant cones
• Categories of unitary representations of Banach-Lie supergroups and restriction functors
• The Gelfand-Naimark-Segal construction for unitary representatins of \mathbb Z₂ⁿ-graded Lie supergroups
• Differentiable vectors and unitary representations of Frechet-Lie\n supergroups
• Finite dimensional compact and unitary Lie superalgebras