We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components and their intersections as well as the construction of an explicit affine paving. Moreover, we compute the ring structure of cohomology by constructing a CW-complex homotopy equivalent to the exotic Springer fiber. This homotopy equivalent space admits an action of the type C Weyl group inducing Kato’s original exotic Springer representation on cohomology. Our results are described in terms of the diagrammatics of the one-boundary Temperley–Lieb algebra (also known as the blob algebra). This provides a first step in generalizing the geometric versions of Khovanov’s arc algebra to the exotic setting.

我们从显式的组合角度研究了对应于单行划分的轨道的奇异Springer光纤的几何形状和拓扑。这包括对不可约成分及其交叉点的结构的详细分析，以及显式仿射铺路的构造。此外，我们通过构建与奇异的Springer光纤等效的CW-复杂同态来计算同调的环结构。这个同态同构空间允许C型Weyl基团的作用，从而引起加藤在同调学上的原始奇异的Springer表示。我们的结果以Temperley-Lieb一边界代数（也称为Blob代数）的图解形式描述。这提供了将Khovanov弧代数的几何形式推广到奇特设置的第一步。