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

摘要

Super coherent states are useful in the explicit construction ofrepresentations of superalgebras and quantum superalgebras. In thiscontribution, we describe how they are used to construct (quantum)boson-fermion realizations and representations of (quantum) superalgebras. Wework through a few examples: $osp(1|2)$ and its quantum version$U_t[osp(1|2)]$, $osp(2|2)$ in the non-standard and standard bases and$gl(2|2)$ in the non-standard basis. We obtain free boson-fermion realizationsof these superalgebras. Applying the boson-fermion realizations, we explicitlyconstruct their finite-dimensional representations. Our results are expected tobe useful in the study of current superalgebras and their correspondingconformal field theories.