Combinatorial bases of modules for affine Lie algebra B_2^(1)

TL;DR

This paper constructs combinatorial bases for modules of the affine Lie algebra B_2^(1) using semi-infinite monomials and vertex operator algebra techniques, advancing the understanding of their structure.

Contribution

It introduces a new method for constructing monomial bases for modules of B_2^(1) using simple currents and intertwining operators, linking to similar bases in A_1^(1).

Findings

Constructed bases of standard modules for B_2^(1) using semi-infinite monomials.

Established a connection between bases of B_2^(1) and A_1^(1) modules.

Provided explicit parametrizations and presentations of the bases.

Abstract

In this paper we construct bases of standard (i.e. integrable highest weight) modules $L(\Lambda)$ for affine Lie algebra of type $B_2\sp{(1)}$ consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces $W(\Lambda)$ of $L(\Lambda)$ by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence $W(k\Lambda_0)$ for $B_2\sp{(1)}$ and the integrable highest weight module $L(k\Lambda_0)$ for $A_1\sp{(1)}$ have the same parametrization of combinatorial bases and the same presentation $\mathcal P/\mathcal I$\,.