4 papers
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…
On components of the tensor square of a Weyl module
Shiliang Gao, Dinglong Wang
For a simple Lie algebra of type or , we give a characterization of the set of dominant integral weights such that for any rational point …
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…
Standard Monomials for Positroid Varieties
Ayah Almousa, Shiliang Gao, Daoji Huang
We give an explicit characterization of the standard monomials for positroid varieties with respect to the Hodge degeneration and give a Gröbner basis. Furthermore, we show that pr…