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Categories of unitary representations of Banach-Lie supergroups and restriction functors
Banach–Lie supergroups unitary representations smooth vectors analytic vectors
2011/8/25
Abstract: We prove that the categories of smooth and analytic unitary representations of Banach--Lie supergroups are well-behaved under restriction functors, in the sense that the restriction of a rep...
Lie supergroups, unitary representations, and invariant cones
Lie supergroups unitary representations invariant cones
2011/1/21
The goal of this article is twofold. First, it presents an application of the theory of invariant convex cones of Lie algebras to the study of unitary rep-resentations of Lie supergroups. Second, it p...
Representation-theoretical Lie supergroups are introduced as supermanifolds with underlying
base manifold being the Lie group associated to the even part of a given Lie superalgebra.
Integrable invariant almost complex structures are introduced in the setting of Lie-Hopf
superalgebras. This leads to a convenient description of the subsheaf of holomorphic
superfunctions in the sh...
Selected results on Lie supergroups and their radial operators
Selected results Lie supergroups radial operators
2011/2/25
Foundational material on complex Lie supergroups and their radial operators is presented. In particular, Berezin’s recursion formula for describing the radial parts of fundamental operators in general...
Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
line operators conformal sigma-models supergroups
2010/12/23
We study line operators in the two-dimensional sigma-model on PSl(n|n) using the current-current OPEs. We regularize and renormalize these line operators, and compute their fusion up to second order ...