Root-theoretic Young diagrams and Schubert calculus II

Abstract: We continue the study of root-theoretic Young diagrams (RYDs) from [Searles-Yong '13]. We provide an RYD formula for the $GL_n$ Belkale-Kumar product, after [Knutson-Purbhoo '11], and we give a translation of the indexing set of [Buch-Kresch-Tamvakis '09] for Schubert varieties of non-maximal isotropic Grassmannians into RYDs. We then use this translation to prove that the RYD formulas of [Searles-Yong '13] for Schubert calculus of the classical (co)adjoint varieties agree with the Pieri rules of [Buch-Kresch-Tamvakis '09], which were needed in the proofs of the (co)adjoint formulas.