Journal of Combinatorics

Volume 7 (2016)

Number 1

Root-theoretic Young diagrams and Schubert calculus II

Pages: 159 – 203

DOI: http://dx.doi.org/10.4310/JOC.2016.v7.n1.a7

Author

Dominic Searles (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Il., USA)

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]. This is needed in the proofs of the (co)adjoint formulas.

Keywords

Belkale–Kumar product, isotropic Grassmannians, Schubert calculus, adjoint varieties

2010 Mathematics Subject Classification

14M15, 14N15

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