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 con-struct representation of superalgebras and quantum superalgebras. Following this stream, we hada contribution to working out explicit representation of Uq[gl(2|1)]. Up to now, Uq[gl(2|1) is stillthe biggest quantum superalgebra representations in coherent state basis of which can be built. Inthis article, we will show some detailed techniques used in our previous work but useful for ourfurther investigations. The newest results on building representations in a coherent state basis ofUq[osp(2|2)], which has the same rank as Uq[gl(2|1)], are also briey exposed