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Highest weight irreducible unitarizable representations of Lie algebras of infinite matrices. The algebra A ∞

Authors

Abstract

In this paper all unitarizable irreducible highest weight representations of the infinite‐dimensional Lie algebra A ∞ , which is a completion and central extension of the general linear Lie algebra gl ∞ , are considered. Within each representation space a basis is introduced and expressions for the transformations of the basis under the action of the Chevalley generators are written.

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Journal

Journal of Mathematical PhysicsAmerican Institute of Physics

Published: May 1, 1990

Keywords: IRREDUCIBLE REPRESENTATIONS; UNITARY SYMMETRY; LIE GROUPS; ALGEBRAS; MATRICES; MANY−DIMENSIONAL CALCULATIONS; TRANSFORMATIONS; EQUATIONS

DOI: 10.1063/1.528786

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