For two elements v and w of the symmetric group S n with v≤ w in Bruhat order, the Bruhat
interval polytope Q v, w is the convex hull of the points (z (1),…, z (n))∈ R n with v≤ z≤ w. It …

Abstract Introduced by Kodama and Williams, Bruhat interval polytopes are generalized
permutohedra closely connected to the study of torus orbit closures and total positivity in …

Let B be a Borel subgroup of GL n (ℂ) and 𝕋 a maximal torus contained in B. Then 𝕋 acts on
GL n (ℂ)∕ B and every Schubert variety is 𝕋-invariant. We say that a Schubert variety is of …

The study of torus orbit closures in the (complete) flag variety was initiated by Klyachko and
Gelfand--Serganova in the mid-1980s, but it seems that not much has been done since then …

We associate a complete non-singular fan with a polygon triangulation. Such a fan appears
from a certain toric Richardson variety, called of Catalan type introduced in this paper. A toric …

To a direct sum of holomorphic line bundles, we can associate two fibrations, whose fibers
are, respectively, the corresponding full flag manifold and the corresponding projective …

A finite Coxeter group W has a natural metric d and if ℳ is a subset of W, then for each u∈
W, there is q∈ ℳ such that d (u, q)= d (u, ℳ). Such q is not unique in general but if ℳ is a …

It is known that for the natural algebraic torus actions on the Grassmannians, the closures of
torus orbits are normal and hence are toric varieties, and that these toric varieties are …

We investigate the class of Kazhdan-Lusztig varieties, and its subclass of matrix Schubert
varieties, endowed with a naturally defined torus action. Writing a matrix Schubert variety …

Introduced by Kodama and Williams, Bruhat interval polytopes are generalized
permutohedra closely connected to the study of torus orbit closures and total positivity in …