New Quiver-Like Varieties and Lie Superalgebras
New Quiver-Like Varieties and Lie Superalgebras
复制标题
DOI：
10.1007/s00220-022-04608-2
复制
发表时间：
2021-05
影响因子：
2.4
通讯作者：
Richárd Rimányi;L. Rozansky
中科院分区：
文献类型：
--
作者：
Richárd Rimányi;L. Rozansky
为了将Yangian R-矩阵的几何化从李代数推广到超代数，我们引入了新的箭图相关簇，这些簇与的表示有关。为了定义它们类似的Nakajima-Cherkis品种，我们重新制定了后者的建设取代汉密尔顿约化与交叉的广义拉格朗日子簇的余切丛坐在顶点的李代数。新的品种来自取代一些拉格朗日子品种与他们的勒让德变换。我们提出了超代数版本的稳定信封的新的箭壶一样的品种，推广了余切丛的格拉斯曼。我们定义了Tarasov-Varchenko权函数的超代数推广，并证明了它们表示超稳定包络。超稳定包络和超权函数都是根据的杨氏矩阵变换的。
In order to extend the geometrization of YangianR-matrices from Lie algebrasto superalgebras, we introduce new quiver-related varieties which are associated with representations of. In order to define them similarly to the Nakajima-Cherkis varieties, we reformulate the construction of the latter by replacing the Hamiltonian reduction with the intersection of generalized Lagrangian subvarieties in the cotangent bundles of Lie algebras sitting at the vertices of the quiver. The new varieties come from replacing some Lagrangian subvarieties with their Legendre transforms. We present superalgebra versions of stable envelopes for the new quiver-like varieties that generalize the cotangent bundle of a Grassmannian. We define superalgebra generalizations of the Tarasov–Varchenko weight functions, and show that they represent the super stable envelopes. Both super stable envelopes and super weight functions transform according to Yangian-matrices ofwith.