Casimir invariants, characteristic identities, and tensor operators for ‘‘strange’’ superalgebras

Abstract

We define a class of (super) subalgebras of gl(m/n) realized as the set of fixed points of a (graded) endomorphism of gl(m/n). This class includes the superalgebras gp(m) and gq(m) [related to the so-called ‘‘strange’’ simple superalgebras p(m) and q(m)], as well as osp(m/n). General covariant, contravariant, and mixed tensor operators are defined for this class in terms of appropriate module homomorphisms. Traces of certain tensors give the usual sequence of Casimir invariants. For gp(m), these are shown to vanish identically, while for gq(m), eigenvalues of the quadratic and cubic Casimir invariants are derived in terms of highest weights and a polynomial characteristic identity is exhibited.