J. Math. Phys. 33, 1841-1863 (1992)

SCI

TRANSFORMATIONS OF SOME INDUCED OSP(3/2) MODULES IN AN SO(3)CIRCLE-PLUS-SP(2) BASIS

N. A. Ky, T. D. Palev, N. I. Stoilova

The modules of the orthosymplectic Lie superalgebra osp(3/2), induced from finite-dimensional irreducible submodules of the stability subalgebra so (3) + gl(1) are investigated. The corresponding infinite-dimensional irreducible or indecomposable modules, the Kac modules, and the related typical and atypical modules are studied in detail. Every such module is decomposed into a direct sum of either indecomposable or irreducible modules of the even subalgebra so (3) + sp(2). For each of these (infinite-dimensional or finite-dimensional, irreducible or indecomposable) modules relations are written down, giving the transformations of the basis under the action of the algebra generators.