Contents Online
Mathematical Research Letters
Volume 23 (2016)
Number 4
Geometric mitosis
Pages: 1071 – 1097
DOI: https://dx.doi.org/10.4310/MRL.2016.v23.n4.a5
Author
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 $Sp_{2n}$.
Keywords
Demazure operator, flag variety, Newton–Okounkov polytope, Schubert calculus
2010 Mathematics Subject Classification
05E10, 14M15, 52B20
Accepted 5 February 2016
Published 16 September 2016