论文标题
量子环形$ \ mathfrak {gl} _1 $的整体形式
An integral form of quantum toroidal $\mathfrak{gl}_1$
论文作者
论文摘要
我们考虑（$ k $的所有$ n $）的（直接总和）的半尼尔德通勤的$ \ mathfrak {gl} _n $的多种多样，并以两种方式描述其卷积代数结构：首先是一个明显的shuffle algebra（即特定的$ \ \ m m iathbbbb {z_____________ 1}] $ - 均值的$ k $ - 一个点的理论），第二个为$ \ m athbb {z} [q_1^{\ pm 1}，q_2^{\ pm 1}] $ - 代数 - 由某些元素$ \ bar {\ bar {\ bar { \ mathbb {n} \ times \ mathbb {z}} $。
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 $\{\bar{H}_{n,d}\}_{(n,d) \in \mathbb{N} \times \mathbb{Z}}$.
