A combinatorial rule for (co)minuscule Schubert calculus
Abstract
We prove a root system uniform, concise combinatorial rule for Schubert calculus of_minuscule_ and_cominuscule_ flag manifolds G/P (the latter are also known as "compact Hermitian symmetric spaces"). We connect this geometry to the poset combinatorics of [Proctor '04], thereby giving a generalization of the [Sch\"{u}tzenberger `77]_jeu de taquin_ formulation of the Littlewood-Richardson rule that computes the intersection numbers of Grassmannian Schubert varieties. Our proof introduces_cominuscule recursions_, a general technique to relate the numbers for different Lie types. A discussion about connections of our rule to (geometric) representation theory is also briefly entertained.
Cite
@article{arxiv.math/0608276,
title = {A combinatorial rule for (co)minuscule Schubert calculus},
author = {Hugh Thomas and Alexander Yong},
journal= {arXiv preprint arXiv:math/0608276},
year = {2010}
}
Comments
23 pages. Companion software available at the authors' websites. v2 is the submitted version, with typo-corrections