Highest-Weight Representations of Sl(2, C) and Sl(3, C) Via Canonical Realizations

摘要

The infinite-dimensional representations of the sl(n+1,C)Lie algebras (maximal representations) constructed in the previous paper are studied on the two simpliest examples n=1.2. The sufficient condition for irreducibility of the maximal representations is proved to be also necessary in these cases. It is further shown that our method allows us to construct other set of infinite-dimensional irreducible highest-weight representations of sl(3,C), the so-called mixed representations, which cover some of the cases when the maximal as well as the standard highest-weight representations (Verma modules) are reducible. (Atomindex citation 11:566437)