Particle basis of Feigin-Stoyanovsky's type subspaces of level $1$ $\tilde{\mathfrak{sl}}_{\ell+1}(\mathbb{C})$-modules

TL;DR

This paper constructs a particle basis for specific subspaces of level 1 modules of affine Lie algebras, leading to explicit character formulas, advancing the combinatorial understanding of these algebraic structures.

Contribution

It introduces a new particle basis for Feigin-Stoyanovsky's subspaces of level 1 modules, enabling explicit character calculations.

Findings

Particle basis construction for subspaces

Derivation of character formulas

Enhanced combinatorial understanding of modules

Abstract

We construct particle basis for Feigin-Stoyanovsky's type subspaces of level $1$ standard $\tilde{\mathfrak{sl}}_{\ell+1}(\mathbb{C})$-modules. From the description we obtain character formulas.