Cherkis bow varieties与affine type $A$的quiver gauge theories的Coulomb branches

蝴蝶结簇稳定包络的存在性与正交性

Existence and orthogonality of stable envelopes for bow varieties

本文综述 A 型蝴蝶结簇的上同调稳定包络，重点证明其存在性与正交性，并以组合化、简化论证支撑显式计算。

有向图初等因子——初等因子映射、有向图初等因子、其欧拉特征和F₁点

Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and $\mathbb{F}_1$-points

本文基于有向图初等因子与映射，研究其欧拉特征及F₁点，通过推广为束并构建模空间，实现复有向图Grassmannian的F₁类比。

Instantons on Gravitons

Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills instantons on ALF gravitational instantons. Our data are formulated in terms of matrix-valued functions of a single variable, that are in turn organized into a bow. We introduce the general notion of a bow, its representation, its associated data and moduli space of solutions. For a judiciously chosen bow the Nahm transform maps any bow solution to an instanton on a…

Cyclotomic double affine Hecke algebras (with an appendix by Hiraku Nakajima and Daisuke Yamakawa)

We show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying reflection group) has four other descriptions: (1) as a subalgebra of the degenerate DAHA of type A given by generators; (2) as an algebra given by generators and relations; (3) as an algebra of differential-reflection operators preserving some spaces of functions; (4) as equivariant Borel-Moore homology of a certain variety. Also, we define a new $q$-deformation of this algebra, which we call cyclotomic DAHA. Namel…