Root-theoretic Young diagrams and Schubert calculus. II. (Q5963390)

In [J. Algebra 448, 238--293 (2016; Zbl 1348.14119)], \textit{A. Yong} and the author study root-theoretic Young diagrams (RYDs), which are one of several natural choices of indexing set for the Schubert present one is that RYDs are useful for studying general patterns in Schubert combinatorics in a uniform manner. The main evidence introduced in that paper is rules for Schubert calculus of the classical (co)adjoint varieties in terms of subvarieties of generalized flag varieties. The thesis of that paper and the RYDs, and a relation between planarity of the root poset for a (co)adjoint variety and polytopalness of the nonzero Schubert structure constants for its cohomology ring. The problem of finding a nonnegative, integral combinatorial rule for the Schubert structure constants of the cohomology ring of a generalized flag variety is longstanding.NEWLINENEWLINEIn this paper they continue the study of root-theoretic Young diagrams (RYDs). They provide an RYD formula for the \(\mathrm{GL}_n/P\) Belkale-Kumar product, and they give a translation of the indexing set of [\textit{A. S. Buch} et al., Invent. Math. 178, No. 2, 345--405 (2009; Zbl 1193.14071)] for Schubert varieties of non-maximal isotropic Grassmannians into RYDs.