Communications in Physics 19, 49-52 (2009)

Gelfand-Tsetlin Basis for Superalgebras and Quantum Superalgebras

Nguyen Anh Ky

The Gel’fand-Tsetlin basis is a powerful tool for constructing finite-dimensional rep- resentations of (classical and quantum) algebras. It turns out that this basis is also useful in constructing representations of superalgebras and quantum superalgebras. An extension of this important basis for this goal is briefly reviewed. In this way, all finite-dimensional representations of a general linear superagebra gl(m/n) and its quantum deformations could be found for any m and n but at the present that can be done only for not very big m and n (because of cumber- some calculations). So far, by this method, all finite-dimensional irreducible representations of some superalgebras such as gl(2/1) and gl(2/2) and their quantum deformations, including the two-parametric deformations introduced by us, have been constructed and classified.