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arXiv · 2209.04852

An integral form of quantum toroidal $\mathfrak{gl}_1$

Andrei Neguţ
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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 $\{\bar{H}_{n,d}\}_{(n,d) \in \mathbb{N} \times \mathbb{Z}}$.

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Andrei Neguţ. 2022-09-11. An integral form of quantum toroidal $\mathfrak{gl}_1$. https://arxiv.org/abs/2209.04852

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