Convex cones and SAGBI bases of permutation invariants

SAGBI bases and Degeneration of Spherical Varieties to Toric Varieties

Let X \subset Proj(V) be a projective spherical G-variety, where V is a finite dimensional G-module and G = SP(2n, C). In this paper, we show that X can be deformed, by a flat deformation, to the toric variety corresponding to a convex polytope Δ(X). The polytope Δ(X) is the polytope fibred over the moment polytope of X with the Gelfand-Cetlin polytopes as fibres. We prove this by showing that if X is a horospherical variety, e.g. flag varieties and Grassmanians, the homogeneous coordinate ring of X can be embedded in a Laurent polynomial algebra and has a SAGBI basis with respect to a natural…

错位排列置换矩阵与轨道调和

Derangement permutation matrices and orbit harmonics

该研究针对错位排列置换矩阵的轨迹，构造轨道调和商环，给出其相伴分次理想的显式生成元，关联希尔伯特级数与Foata变换等，还得到其分次对称群特征的交替和公式，证明用到同调代数映射锥构造。