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arXiv · 2103.16197

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

Narasimha Chary Bonala·Oliver Clarke·Fatemeh Mohammadi
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Abstract

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 toric degenerations of Richardson varieties. In particular, we provide a new family of toric degenerations of Richardson varieties inside flag varieties.

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Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi. 2021-03-30. Standard monomial theory and toric degenerations of Richardson varieties in flag varieties. https://arxiv.org/abs/2103.16197

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