Combinatorial bases of principal subspaces for affine Lie algebra of type B_2^(1)

TL;DR

This paper constructs combinatorial bases for principal subspaces of affine Lie algebra of type B2^(1) using vertex operator algebra theory, leading to explicit character formulas.

Contribution

It introduces new quasi-particle bases for principal subspaces of affine B2^(1) modules, enabling explicit character formulas.

Findings

Constructed combinatorial bases for principal subspaces.

Derived explicit character formulas from the bases.

Connected bases to quasi-particle theory.

Abstract

We consider principal subspaces $W_{L(k\Lambda_0)}$ and $W_{N(k\Lambda_0)}$ of standard module $L(k\Lambda_0)$ and generalized Verma module $N(k\Lambda_0)$ at level $k\geq 1$ for affine Lie algebra of type $B_2^{(1)}$. By using the theory of vertex operator algebras, we find combinatorial bases of principal ubspaces in terms of quasi-particles. From quasi-particle bases, we obtain character formulas for $W_{L(k\Lambda_0)}$ and $W_{N(k\Lambda_0)}$.