Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux. (May 2021)

• Record Type: Journal Article
• Authors: Clarke, Oliver; Mohammadi, Fatemeh
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 683
• Page End: 723
• Publication Date: 2021-05
• Subjects: Toric degenerations -- Flag varieties -- Schubert varieties -- Semi-standard tableaux; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.09.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We study Gröbner degenerations of Schubert varieties inside flag varieties. We consider toric degenerations of flag varieties induced by matching fields and semi-standard Young tableaux. We describe an analogue of matching field ideals for Schubert varieties inside the flag variety and give a complete characterization of toric ideals among them. We use a combinatorial approach to standard monomial theory to show that block diagonal matching fields give rise to toric degenerations. Our methods and results use the combinatorics of permutations associated to Schubert varieties, matching fields and their corresponding tableaux.