Representations of quantum toroidal superalgebras and plane s-partitions

2021/04/12 by Luan Bezerra, E. Mukhin, Bezerra, Luan +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2104.05841

openalex publication_date 2021/04/12 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28

Abstract

We construct Fock and MacMahon modules for the quantum toroidal superalgebra E_s associated with the Lie superalgebra \mathfrakgl_m|n and parity s. The bases of the Fock and MacMahon modules are labeled by super-analogs of partitions and plane partitions with various boundary conditions, while the action of generators of E_s is given by Pieri type formulas. We study the corresponding characters.

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