Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions

We consider the conormal bundle of a Schubert variety $S_I$ in the cotangent bundle $T^* Gr$ of the Grassmannian $Gr$ of $k$-planes in $C^n$. This conormal bundle has a fundamental class ${κ_I}$ in the equivariant cohomology $H^*_{T}(T^* Gr)$. Here $T=(C^*)^n\times C^*$. The torus $(C^*)^n$ acts on $T^* Gr$ in the standard way and the last factor $C^*$ acts by multiplication on fibers of the bundle. We express this fundamental class as a sum $Y_I$ of the Yangian $Y(gl_2)$ weight functions $(W_J)_J$. We describe a relation of $Y_I$ with the double Schur polynomial $[S_I]$. A modified version of…

论例外格拉斯曼流形及其幂零簇

On the exotic Grassmannian and its nilpotent variety

本研究针对对称对$(\mathrm{GL}(V),\mathrm{GL}(V_1)\times\mathrm{GL}(V_2))$的双旗簇，借助余法簇建立其$K$-轨道与例外幂零锥$K$-轨道的几何对应，给出特殊情形的组合解释，灵感源于经典与近期相关研究。

拉格朗日格拉斯曼流形、CKP 层次结构与超行列式关系

Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations

本文研究拉格朗日格拉斯曼流形几何与 CKP 可积层次结构的关系，通过扩展至无穷维并引入费米子 Fock 空间，推导出超行列式关系的无穷维类似形式及多参数族。