Following Schubert varieties under Feigin's degeneration of the flag variety (Q6570597)

Let \(G\) be a complex simple Lie group and let \(P \subset G\) be a parabolic subgroup. Feigin introduced a flat degeneration of the flag variety \(G/P\), which is equipped with an action of the \(M\)-fold product of the additive group of the field, with \(M\) being the dimension of a maximal unipotent subgroup of \(G\).\N\NThe authors study the effect of Feigin's flat degeneration of the type A flag variety on the defining ideals of its Schubert varieties. They describe two classes of Schubert varieties which stay irreducible under the degenerations and in several cases, they are able to encode reducibility of the degenerations in terms of symmetric group combinatorics. The authors also obtain an identification of some degenerate Schubert varieties (i.e. the vanishing sets of initial ideals of the ideals of Schubert varieties with respect to Feigin's Groebner degeneration) with Richardson varieties in higher rank partial flag varieties.