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Casimir invariants and characteristic identities for gl(∞ )

M. D. Gould, N. I. Stoilova

math-pharXiv:physics/9612009

Abstract

A full set of (higher order) Casimir invariants for the Lie algebra gl(∞ ) is constructed and shown to be well defined in the category OFS generated by the highest weight (unitarizable) irreducible representations with only a finite number of non-zero weight components. Moreover the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(∞ ) are also determined and generalize those previously obtained for gl(n) by Bracken and Green.1,2

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