Eigenvalues of Casimir invariants for type I quantum superalgebras

Abstract

We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.Mathematics Subject Classifications 81R10, 17B37, 16W30

Solution of a supersymmetric model of correlated electrons

“…However, at least from the Bethe ansatz point of view, there exists a supersymmetric solution which has not yet been discussed in the literature so far. This solution was found sometime ago by Deguchi et al [12] in the context of a q-deformed Osp(2|2) superalgebra and very recently has been interpreted as being invariant by the twisted U q [Sl(2|2) (2) ] superalgebra [13]. It seems that this model exhausts the cases which can be derived by exploiting the Osp(2|2) superalgebra [9,13].…”

Eigenvalues of Casimir invariants for Uq[osp(m∣n)]

“…This had already been done for U q ͓osp͑2 ͉ n͔͒, using a different method, in Ref. 12. Also every finite-dimensional representation of U q ͓osp͑1 ͉ n͔͒ is isomorphic to a finite-dimensional representation of U −q ͓o͑n +1͔͒, 14 whose central elements are well understood.…”

An explicit construction of Casimir operators and eigenvalues. I

“…It will be instructive to show here that how invariance, parity, duality and Weyl-symmetry properties reduce the number of coefficients before solving them from (II.6). It is clear, for instance, that g 1,2,3,25 fulfills the invariance property while its equivalents are g 1,2,3,25 ∼ g 10,16,17,18 , g 1,2,3,25 ∼ g 3,4,5,27 due respectively to parity and duality properties. It has also several equivalents under the actions of Weylsymmetry.…”