A new class of unitarizable highest weight representations of infinite dimensional Lie algebras. (English) Zbl 0581.17009

Jakobsen, H. P.; Kac, V. G.

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

Keywords:

Kac-Moody algebras; affine algebras; infinite dimensional Lie algebras; unitarizable highest weight representation