# Standard monomial theory and toric degenerations of Richardson varieties in flag varieties

@inproceedings{Bonala2021StandardMT, title={Standard monomial theory and toric degenerations of Richardson varieties in flag varieties}, author={Narasimha Chary Bonala and Oliver Clarke and Fatemeh Mohammadi}, year={2021} }

We study standard monomial bases for Richardson varieties inside the flag variety. In general, writing down a standard monomial basis for a Richardson variety can be challenging, as it involves computing so-called defining chains or key tableaux. However, for a certain family of Richardson varieties, indexed by compatible permutations, we provide a very direct and straightforward combinatorial rule for writing down a standard monomial basis. We apply this result to the study of toricβ¦Β Expand

#### One Citation

Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian

- Mathematics
- 2021

Richardson varieties are obtained as intersections of Schubert and opposite Schubert varieties. We provide a new family of toric degenerations of Richardson varieties inside Grassmannians by studyingβ¦ Expand

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Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian

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