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

TL;DR

This paper constructs combinatorial bases for certain subspaces of affine Lie algebra modules, proving their spanning and linear independence using advanced algebraic tools, thereby advancing the understanding of these algebraic structures.

Contribution

It introduces explicit combinatorial bases for Feigin-Stoyanovsky's type subspaces of $C_^{(1)}$ modules, utilizing annihilating fields, simple currents, and intertwining operators.

Findings

Constructed explicit combinatorial bases for subspaces.

Proved spanning property using annihilating fields.

Established linear independence via fusion rule techniques.

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.