Integrating Unitary Representations of Infinite-Dimensional Lie Groups

2001/06/23 by Valerio Toledano-Laredo · 2 citations
Mathematics · #math.RT #math.FA #math.QA

paper · pdf

published as Journal of Functional Analysis 161, 1999, 478-508 · Available from Academic Press at http://www.academicpress.com/jfa

arxiv created 2001/06/23 · arxiv updated 2009/11/30

Abstract

We show that in the presence of suitable commutator estimates, a projective unitary representation of the Lie algebra of a connected and simply connected Lie group G exponentiates to G. Our proof does not assume G to be finite--dimensional or of Banach-Lie type and therefore encompasses the diffeomorphism groups of compact manifolds. We obtain as corollaries short proofs of Goodman and Wallach's results on the integration of positive energy representations of loop groups and Diff(S¹) and of Nelson's criterion for the exponentiation of unitary representations of finite-dimensional Lie algebras.

Cited by

• Integrating positive energy representations of the Virasoro algebra
• Conformal nets from minimal W-algebras

Related

• Semi-bounded unitary representations of infinite-dimensional Lie groups
• Bounded and Semi-bounded Representations of Infinite Dimensional Lie\n Groups
• Equivalence of the Brownian and energy representations
• Finite dimensional compact and unitary Lie superalgebras
• Hodge theory and unitary representations, in the example of SL(2,ℝ)