CASIMIR INVARIANTS AND CHARACTERISTIC IDENTITIES FOR GL(INFINITY)

A full set of (higher-order) Casimir invariants for the Lie algebra gl (infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible repre sentations with only a finite number of nonzero weight components. Mor eover, the eigenvalues of these Casimir invariants are determined expl icitly in terms of the highest weight. Characteristic identities satis fied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American In stitute of Physics.