光滑 Nakajima 箭簇簇仿射化的 Namikawa-Weyl 群

Monomials of q and q,t-characters for non simply-laced quantum affinizations

Nakajima introduced the morphism of q,t-characters for finite dimensional representation of simply-laced quantum affine algebras : it is a t-deformation of the Frenkel-Reshetikhin's morphism of q-characters (sum of monomials in infinite variables). In math.QA/0212257 we generalized the construction of q,t-characters for non simply-laced quantum affine algebras. First in this paper we prove a conjecture of math.QA/0212257 : the monomials of q and q,t-characters of standard representations are the same in non simply-laced cases (the simply-laced cases were treated by Nakajima) and the coefficien…

对称箭形簇与临界稳定包络

Symmetric quiver varieties and critical stable envelopes

本文研究了对称箭形簇的几何性质，证明其行为类似于普遍变形的Nakajima箭形簇，并通过双曲限制提供了临界稳定包络的新证明。

关于幂零轨道与抛物 Slodowy 簇的 Hikita-Nakajima 猜想

Around Hikita-Nakajima conjecture for nilpotent orbits and parabolic Slodowy varieties

本文针对幂零 Slodowy 横截与特殊幂零轨道覆盖的辛对偶，修正原始 Hikita 猜想，并对抛物 Slodowy 簇证明其成立，同时给出李理论与组合应用。

Smallness problem for quantum affine algebras and quiver varieties

The geometric small property (Borho-MacPherson) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima (math.QA/0105173) for certain resolutions of quiver varieties (analogs of the Springer resolution) : for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination theorem for monomials of Frenkel-Reshetikhin q-characters that we establish for non necessarily…

通过临界稳定包络发展移位的量子群

Shifted quantum groups via critical stable envelopes

本文通过临界稳定包络构造移位量子群，并将其与临界上同调Hall代数联系起来，扩展了Nakajima有向图变体的结果到临界情形。

通过箭图簇的拟经典Braverman--Kazhdan交织子

Quasi-Classical Braverman--Kazhdan Intertwiners via Quiver Varieties

构造了Braverman--Kazhdan空间余切丛的仿射化之间的同构，证明了SL_n×L^{ab}-等变性和辫关系，作为Braverman--Kazhdan归一化交织算子的拟经典极限，通过定义SL-规范群箭图簇的反射函子推广了Gelfand--Graev作用的构造。