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An integral form of quantum toroidal $\mathfrak{gl}_1$ (2209.04852v1)
Published 11 Sep 2022 in math.QA and math.RT
Abstract: We consider the (direct sum over all $n$ of the) $K$-theory of the semi-nilpotent commuting variety of $\mathfrak{gl}n$, and describe its convolution algebra structure in two ways: the first as an explicit shuffle algebra (i.e. a particular $\mathbb{Z}[q_1{\pm 1}, q_2{\pm 1}]$-submodule of the equivariant $K$-theory of a point) and the second as the $\mathbb{Z}[q_1{\pm 1}, q_2{\pm 1}]$-algebra generated by certain elements ${\bar{H}{n,d}}_{(n,d) \in \mathbb{N} \times \mathbb{Z}}$.