Affinization of shifted quantum affine \mathfrakgl₂

2025/11/15 by Boris Feigin, Feigin, B., M. Jimbo +3
Mathematics · #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2511.12178

Abstract

We give a realization A₀ of quantum toroidal algebra associated to \mathfrakgl₂ which can be viewed as an affinization of the Drinfeld new realization of quantum affine \mathfrakgl₂. We use this realization to define an affinization A_N, N∈\mathbb Z, of shifted quantum affine \mathfrakgl₂. We construct a large family of representations of dominantly shifted algebra \mathcal A_N, N>0. The examples of representations with even positive N appear in the study of extensions of deformed W-algebras of type \mathfrakgl(N+2|1).

Citations

• Extensions of deformed W-algebras via qq-characters
• Representations of quantum toroidal gl_n

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