Free field realization of the quantum toroidal algebra of \mathfrakgl₁ with general levels

2025/04/24 by Chen, Zitao, Ding, Xiang-Mao
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.17508

Abstract

We present a unified free field realization of representations for the quantum toroidal algebra of \mathfrakgl₁ 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 \mathfrakgl₁. Utilizing this free field realization, we further develop intertwining operators for the quantum toroidal algebra of \mathfrakgl₁.

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Related

• Representations of quantum toroidal gl_n
• The PBW basis of U_q,q(\mathfrakgl_n)
• The R-matrix of the quantum toroidal algebra
• Quantum toroidal and shuffle algebras
• An integral form of quantum toroidal \mathfrakgl₁