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.

20 pages, 7 figures