Deformation of current algebras in \(3+1\) dimensions
In a previous paper [Commun. Math. Phys. 116, 365-400 (1988; Zbl 0648.22013)], the authors attempted to construct a unitary representation of the group XG of maps from a compact 3-manifold X into a compact Lie group G by embedding XG into an infinite-dimensional general linear group \(GL_ 2\). However, it turned out that the representations constructed were not, in fact, unitary. In the present paper, the authors construct a 3-parameter deformation of (the universal central extension of) the Lie algebra of \(GL_ 2\), together with representations which are unitary for certain values of the deformation parameter.
highest-weight nonunitary representations
scientific article; zbMATH DE number 4202534