Highest Weight Representations of the Lie Algebra gl∞ in a Gel’fand-Zetlin Basis

Abstract

In the last few years the algebra gl∞ of infinite matrices is of increasing interest in physics. The reason for this stems from the observation that the irreducible gl∞ modules appear as natural carrier spaces for Virasoro algebras, loop algebras and Kac-Moody algebras [1]. Therefore, the gl∞ modules provide a natural background for study of various physical applications of the algebras, mentioned above [2].