On the coherent state method in constructing representations of quantum superalgebras

In recent years, one of the new applications of the coherent state method was to construct representation of superalgebras and quantum superalgebras. Following this stream, we had a contribution to working out explicit representation of Uq[gl(2|1)]. Up to now, Uq[gl(2|1) is still the biggest quantum superalgebra representations in coherent state basis of which can be built. In this article, we will show some detailed techniques used in our previous work but useful for our further investigations. The newest results on building representations in a coherent state basis of Uq[osp(2|2)], which has the same rank as Uq[gl(2|1)], are also briefly exposed. (author)