Combinatorial bases in quantum toroidal \mathfrakgl₂ modules

2024/03/25 by Michio Jimbo, E. Mukhin, Jimbo, Michio +1
Materials Science · Mathematics · #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nanocluster Synthesis and Applications #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2403.16705

openalex publication_date 2024/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that many tame modules of the quantum toroidal \mathfrakgl₂ algebra can be explicitly constructed in a purely combinatorial way using the theory of q-characters. The examples include families of evaluation modules obtained from analytic continuation and automorphism twists of Verma modules of the quantum affine \mathfrakgl₂ algebra. The combinatorial bases in the modules are labeled by colored plane partitions with various properties.

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