Representations of quantum toroidal superalgebras and plane $\mathbf{s}$-partitions

Luan Bezerra; Evgeny Mukhin

Representations of quantum toroidal superalgebras and plane $\mathbf{s}$-partitions

Quantum Algebra 2023-12-21 v2 Representation Theory

Authors: Luan Bezerra , Evgeny Mukhin

Abstract

We construct Fock and MacMahon modules for the quantum toroidal superalgebra $\mathcal{E}_\mathbf{s}$ associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$ and parity $\mathbf{s}$ . 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 $\mathcal{E}_\mathbf{s}$ is given by Pieri type formulas. We study the corresponding characters.

Keywords

quantum toroidal superalgebra fock modules macmahon modules lie superalgebra plane partitions pieri formulas characters

Cite

@article{arxiv.2104.05841,
  title  = {Representations of quantum toroidal superalgebras and plane $\mathbf{s}$-partitions},
  author = {Luan Bezerra and Evgeny Mukhin},
  journal= {arXiv preprint arXiv:2104.05841},
  year   = {2023}
}

Comments

v1: Latex, 42 pages, 14 figures. v2: minor corrections. Comments are welcome!

Representations of quantum toroidal superalgebras and plane $\mathbf{s}$-partitions

Abstract

Keywords

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