Resumen de Degenerate coordinate rings of flag varieties and Frobenius splitting

Chuck Hague

• Recently E. Feigin introduced the GN a -degenerations of semisimple algebraic groups and their associated degenerate flag varieties. It has been shown by Feigin, Finkelberg, and Littelmann that the degenerate flag varieties in types An and Cn are Frobenius split. In this paper, we construct an associated degeneration of homogeneous coordinate rings of classical flag varieties in all types and show that these rings are Frobenius split in most types. It follows that the degenerate flag varieties of types An,Cn, and G2 are Frobenius split. In particular, we obtain an alternate proof of splitting in types An and Cn; the case G2 was not previously known. We also give a representation-theoretic condition on PBW-graded versions of Weyl modules which is equivalent to the existence of a Frobenius splitting of the classical flag variety that maximally compatibly splits the identity