Super Coherent States, Boson-Fermion Realizations and Representations of Superalgebras

Super coherent states are useful in the explicit construction of representations of superalgebras and quantum superalgebras. In this contribution, we describe how they are used to construct (quantum) boson-fermion realizations and representations of (quantum) superalgebras. We work through a few examples: $osp(1\mathrm{\mid }2)$ and its quantum version $U_t[osp(1\mathrm{\mid }2)]$, $osp(2\mathrm{\mid }2)$ in the non-standard and standard bases and $gl(2\mathrm{\mid }2)$ in the non-standard basis. We obtain free boson-fermion realizations of these superalgebras. Applying the boson-fermion realizations, we explicitly construct their finite-dimensional representations. Our results are expected to be useful in the study of current superalgebras and their corresponding conformal field theories.