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- W4380136648 abstract "We define and study the shuffle algebra $Sh_{m|n}$ of the quantum toroidal algebra $mathcal E_{m|n}$ associated to Lie superalgebra $mathfrak{gl}_{m|n}$. We show that $Sh_{m|n}$ contains a family of commutative subalgebras $mathcal B_{m|n}(s)$ depending on parameters $s=(s_1,dots,s_{m+n})$, $prod_i s_i=1$, given by appropriate regularity conditions. We show that $mathcal B_{m|n}(s)$ is a free polynomial algebra and give explicit generators which conjecturally correspond to the traces of the $s$-weighted $R$-matrix computed on the degree zero part of $mathcal E_{m|n}$ modules of levels $pm 1$." @default.
- W4380136648 created "2023-06-10" @default.
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- W4380136648 date "2023-06-08" @default.
- W4380136648 modified "2023-09-24" @default.
- W4380136648 title "Commutative subalgebra of a shuffle algebra associated with quantum toroidal $mathfrak{gl}_{m|n}$" @default.
- W4380136648 doi "https://doi.org/10.48550/arxiv.2306.05223" @default.
- W4380136648 hasPublicationYear "2023" @default.
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