Casimir invariants and characteristic identities for $gl(\infty )$

Details Casimir invariants and characteristic identities for $gl(\infty )$ Casimir invariants and characteristic identities for $gl(\infty )$

1996-12-12

arxiv.org/abs/physics/9612009v1

J.Math.Phys. 38 (1997) 4783-4793

Physics

Mathematical Physics

10 pages, PlainTex

Scientific paper

10.1063/1.532123

A full set of (higher order) Casimir invariants for the Lie algebra $gl(\infty )$ is constructed and shown to be well defined in the category $O_{FS}$ 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 $gl(\infty )$ are also determined and generalize those previously obtained for $gl(n)$ by Bracken and Green.$^{1,2}$

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