Indecomposable representations of the algebra su(2,1)

Research paper by Yu. F. Smirnov, Bruno Gruber

Indexed on: 01 Sep '80Published on: 01 Sep '80Published in: Letters in Mathematical Physics

Abstract

Representations of the Lie algebra sl(3) with highest weight are analyzed. Invariant subspaces of indecomposable representations are determined. We study the decomposition of these representations with respect to the subalgebras su(2) and su(1,1) (in their obvious imbedding in su(2,1)).For special cases this decomposition gives indecomposable non multiplicity free representations (indecomposable pairs) with highest weight. These were discussed in [1] and appear also in the decomposition so(3,2) ⊃ su(1,1) of the Rac representation, [7].