# W-translated Schubert divisors and transversal intersections

@article{Hwang2022WtranslatedSD, title={W-translated Schubert divisors and transversal intersections}, author={Dongseon Hwang and Hwayoung Lee and Jae-Hyouk Lee and Changzheng Li}, journal={Science China Mathematics}, year={2022}, volume={65}, pages={1997 - 2018} }

We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety Fℓn1,…,nk;n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F{\ell _{{n_1}, \ldots,{n_k};n}}$$\end{document} via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions…

## References

SHOWING 1-10 OF 41 REFERENCES

### Schubert Geometry of Flag Varieties and Gelfand-Cetlin Theory

- Mathematics
- 2000

This thesis investigates the connection between the geometry of Schubert varieties and Gelfand-Cetlin coordinates on ag manifolds. In particular, we discovered a connection between Schubert calculus…

### Projections of Richardson Varieties

- Mathematics
- 2010

While the projections of Schubert varieties in a full generalized flag manifold G/B to a partial flag manifold $G/P$ are again Schubert varieties, the projections of Richardson varieties…

### A geometric Littlewood-Richardson rule

- Mathematics
- 2003

We describe a geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties into the union of Schubert varieties. There are no restrictions on the base…

### Mirror symmetry and toric degenerations of partial flag manifolds

- Mathematics
- 1998

In this paper we propose and discuss a mirror construction for complete intersections in partial flag manifolds F (n1, . . . , nl, n). This construction includes our previous mirror construction for…

### Note on cohomology rings of spherical varieties and volume polynomial

- Mathematics
- 2003

Let G be a complex reductive group and X a projective spherical G-variety. Moreover, assume that the subalgebra A of the cohomology ring H^*(X, R) generated by the Chern classes of line bundles has…

### Gelfand–Zetlin polytopes and flag varieties

- Mathematics
- 2009

I construct a correspondence between the Schubert cycles on the variety of complete flags in ℂ n and some faces of the Gelfand-Zetlin polytope associated with the irreducible representation of SL n…

### A Littlewood–Richardson rule for two-step flag varieties

- Mathematics
- 2008

This paper studies the geometry of one-parameter specializations of subvarieties of Grassmannians and two-step flag varieties. As a consequence, we obtain a positive, geometric rule for expressing…

### An analogue of the Hodge-Riemann relations for simple convex polytopes

- Mathematics
- 1999

ContentsIntroduction § 1. Combinatorics of simple polytopes1.1. Simple polytopes1.2. The Dehn-Sommerville equations1.3. Stanley's theorem1.4. Kahler manifolds1.5. The Hodge-Riemann form on a Kahler…