Recurrence relations for characters of affine Lie algebra $A_{\ell}^{(1)}$

TL;DR

This paper derives recurrence relations for the characters of certain subspaces of affine Lie algebra modules, using combinatorial bases and intertwining operators, advancing the understanding of their structure.

Contribution

It introduces new recurrence relations for characters of Feigin-Stoyanovsky's subspaces of affine Lie algebra modules at fixed level.

Findings

Derived exact sequences of subspaces

Established systems of recurrence relations

Enhanced understanding of module characters

Abstract

By using the known description of combinatorial bases for Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebra $\mathfrak{sl}(l+1,\mathbb{C})^{\widetilde{}}$, as well as certain intertwining operators between standard modules, we obtain exact sequences of Feigin-Stoyanovsky's type subspaces at fixed level $k$. This directly leads to systems of recurrence relations for formal characters of those subspaces.