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A new class of unitarizable highest weight representations of infinite dimensional Lie algebras. (English) Zbl 0581.17009
Non-linear equations in classical and quantum field theory, Proc. Semin., Paris 1983-1984, Lect. Notes Phys. 226, 1-20 (1985).
[For the entire collection see Zbl 0559.00019.]
Unitarizable highest weight representations of infinite dimensional Lie algebras over the complex number field are studied. Recall that any highest weight representation determines a Hermitian form. If this form is positive definite, the representation is called unitarizable. In this paper the unitarizable highest weight representation of the Lie algebra $$sl_ 2({\mathbb{C}}[z,z^{-1}])$$ is found.
Reviewer: A.G.Gejn

##### MSC:
 17B65 Infinite-dimensional Lie (super)algebras 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B15 Representations of Lie algebras and Lie superalgebras, analytic theory