Journal of Combinatorics
Volume 7 (2016)
Root-theoretic Young diagrams and Schubert calculus II
Pages: 159 – 203
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]. This is needed in the proofs of the (co)adjoint formulas.
Belkale–Kumar product, isotropic Grassmannians, Schubert calculus, adjoint varieties
2010 Mathematics Subject Classification