Free field realization of the quantum toroidal algebra of $\mathfrak{gl}_1$ with general levels
Zitao Chen, Xiang-Mao Ding
公開日: 2025/4/24
Abstract
We present a unified free field realization of representations for the quantum toroidal algebra of $\mathfrak{gl}_1$ with arbitrary levels, constructed using six free boson fields. This realization arises from a specialized factorization of the structure function within the defining relations of the quantum toroidal algebra of $\mathfrak{gl}_1$. Utilizing this free field realization, we further develop intertwining operators for the quantum toroidal algebra of $\mathfrak{gl}_1$.