Geometric mitosis
Algebraic Geometry
2019-02-08 v1 Representation Theory
Abstract
We describe an elementary convex geometric algorithm for realizing Schubert cycles in complete flag varieties by unions of faces of polytopes. For GL_n and Gelfand--Zetlin polytopes, combinatorics of this algorithm coincides with that of the mitosis on pipe dreams introduced by Knutson and Miller. For Sp_4 and a Newton--Okounkov polytope of the symplectic flag variety, the algorithm yields a new combinatorial rule that extends to Sp_{2n}.
Cite
@article{arxiv.1409.6097,
title = {Geometric mitosis},
author = {Valentina Kiritchenko},
journal= {arXiv preprint arXiv:1409.6097},
year = {2019}
}
Comments
19 pages