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

@article{Bonala2021StandardMT,
  title={Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian},
  author={Narasimha Chary Bonala and Oliver Clarke and Fatemeh Mohammadi},
  journal={Journal of Algebraic Combinatorics},
  year={2021},
  pages={1-25}
}
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 studying Grobner degenerations of their corresponding ideals. These degenerations are parametrised by block diagonal matching fields in the sense of Sturmfels [33]. We associate a weight vector to each block diagonal matching field and study its corresponding initial ideal. In particular, we characterise… Expand
2 Citations
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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 involvesExpand
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