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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Acknowledgements
NC was supported by the SFB/TRR 191 “Symplectic structures in Geometry, Algebra and Dynamics”. He gratefully acknowledges support from the Max Planck Institute for Mathematics in Bonn, and the EPSRC Fellowship EP/R023379/1 who supported his multiple visits to Bristol. OC was supported by EPSRC Doctoral Training Partnership award EP/N509619/1. FM was supported by EPSRC Fellowship EP/R023379/1, the BOF grant BOF/STA/201909/038, and the FWO (project no. G023721N and G0F5921N).
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Bonala, N.C., Clarke, O., Mohammadi, F. (2021). Standard Monomial Theory and Toric Degenerations of Richardson Varieties in Flag Varieties. In: Miller, C., Striuli, J., Witt, E.E. (eds) Women in Commutative Algebra. Association for Women in Mathematics Series, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-030-91986-3_6
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DOI: https://doi.org/10.1007/978-3-030-91986-3_6
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