Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux

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