Root-theoretic Young diagrams and Schubert calculus II
Combinatorics
2013-11-13 v1 Algebraic Geometry
Abstract
We continue the study of root-theoretic Young diagrams (RYDs) from [Searles-Yong '13]. We provide an RYD formula for the 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.
Cite
@article{arxiv.1311.2884,
title = {Root-theoretic Young diagrams and Schubert calculus II},
author = {Dominic Searles},
journal= {arXiv preprint arXiv:1311.2884},
year = {2013}
}
Comments
29 pages