Casimir invariants and characteristic identities for $gl(\infty )$
Gould, M. D. ; Stoilova, N. I.
arXiv, 9612009 / Harvested from arXiv
Text on arXiv
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.$^{1,2}$
Publié le : 1996-12-12
Classification:  Mathematical Physics 
@article{9612009,
     author = {Gould, M. D. and Stoilova, N. I.},
     title = {Casimir invariants and characteristic identities for $gl(\infty )$},
     journal = {arXiv},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9612009}
}

Gould, M. D.; Stoilova, N. I. Casimir invariants and characteristic identities for $gl(\infty )$. arXiv, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/9612009/