Bases of Feigin-Stoyanovsky's type subspaces for $C_\ell^{(1)}$

Abstract

In this paper we construct combinatorial bases of Feigin-Stoyanovsky's type subspaces of standard modules for level $k$ affine Lie algebra $C_\ell^{(1)}$. We prove spanning by using annihilating field $x_\theta (z)^{k+1}$ of standard modules. In the proof of linear independence we use simple currents and intertwinining operators whose existence is given by fusion rules.