Bases of Feigin–Stoyanovsky’s type subspaces for $$C_\ell ^{(1)}$$ C ℓ ( 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 intertwining operators whose existence is given by fusion rules.