Linear independence for $C_{\ell }^{(1)}$ by using $C_{2\ell }^{(1)}$

Abstract

In this note we prove linear independence of the combinatorial spanning set for standard $C_{\ell }^{(1)}$-module $L(k\hat{I}{›}_0)$ by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace $W(k\hat{I}{›}_0)$ of $C_{2\ell }^{(1)}$-module $L(k\hat{I}{›}_0)$. It should be noted that the proof of linear independence for the basis of $W(k\hat{I}{›}_0)$ is obtained by using simple currents and intertwining operators in the vertex operator algebra $L(k\hat{I}{›}_0)$.

13 pages, 9 figures