Presentations of Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebras of type $C_{\ell }^{(1)}$

Abstract

Feigin-Stoyanovsky's type subspace $W(\Lambda )$ of a standard $\tilde{\mathfrak{g}}$-module $L(\Lambda )$ is a ${\tilde{\mathfrak{g}}}_1$-submodule of $L(\Lambda )$ generated by the highest-weight vector $v_{\Lambda }$, where ${\tilde{\mathfrak{g}}}_1$ is a certain commutative subalgebra of $\tilde{\mathfrak{g}}$. Based on the description of basis of $W(\Lambda )$ for $\tilde{\mathfrak{g}}$ of type $C_{\ell }^{(1)}$, we give a presentation of this subspace in terms of generators and relations $$W(\Lambda )\simeq U({\tilde{\mathfrak{g}}}_1^{-})/J.$$

References in corpus (1)

• Intertwining vertex operators and certain representations of sl(n)^