5 papers
Lattice Bruhat intervals are polytopal
Yibo Gao, Tao Gui
For a Bruhat interval in an arbitrary Coxeter group which is a lattice, we give a type-uniform construction of a convex polytope whose complete face lattice realizes $[x,y]…
Tilted Richardson Varieties
Jiyang Gao, Shiliang Gao, Yibo Gao
The study of the flag variety and its subvarieties, including Schubert and Richardson varieties, plays a fundamental role in algebraic geometry and algebraic combin…
Introduction to the Cohomology of the Flag Variety
Sara C. Billey, Yibo Gao, Brendan Pawlowski
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumer…
Orbit structures and complexity in Schubert and Richardson Varieties
Yibo Gao, Reuven Hodges
The goal of this paper is twofold. Firstly, we provide a type-uniform formula for the torus complexity of the usual torus action on a Richardson variety, by developing the notion o…
Quantum Bruhat graphs and tilted Richardson varieties
Jiyang Gao, Shiliang Gao, Yibo Gao
Quantum Bruhat graph is a weighted directed graph on a finite Weyl group first defined by Brenti-Fomin-Postnikov. It encodes quantum Monk's rule and can be utilized to study the $3…