Shuffle algebras for quivers as quantum groups
Shuffle algebras for quivers as quantum groups
复制标题
将箭袋的代数打乱为量子群
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
O. Schiffmann
中科院分区：
文献类型：
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作者：
Andrei Neguct;Francesco Sala;O. Schiffmann
We define a quantum loop group $mathbf{U}^+_Q$ associated to an arbitrary quiver $Q=(I,E)$ and maximal set of deformation parameters, with generators indexed by $I imes mathbb{Z}$ and some explicit quadratic and cubic relations. We prove that $mathbf{U}^+_Q$ is isomorphic to the (generic, small) shuffle algebra associated to the quiver $Q$ and hence, by [Neg21a], to the localized K-theoretic Hall algebra of $Q$. For the quiver with one vertex and $g$ loops, this yields a presentation of the spherical Hall algebra of a (generic) smooth projective curve of genus $g$ (invoking the results of [SV12]). We extend the above results to the case of non-generic parameters satisfying a certain natural metric condition. As an application, we obtain a description by generators and relations of the subalgebra generated by absolutely cuspidal eigenforms of the Hall algebra of an arbitrary smooth projective curve (invoking the results of [KSV17]).
影响因子：
3.1
作者：
A. Okounkov;A. Smirnov
通讯作者：
A. Okounkov;A. Smirnov