Skip to Main content Skip to Navigation
Conference papers

Total positivity for cominuscule Grassmannians

Abstract : In this paper we explore the combinatorics of the non-negative part $(G/P)_{\geq 0}$ of a cominuscule Grassmannian. For each such Grassmannian we define Le-diagrams ― certain fillings of generalized Young diagrams which are in bijection with the cells of $(G/P)_{\geq 0}$. In the classical cases, we describe Le-diagrams explicitly in terms of pattern avoidance. We also define a game on diagrams, by which one can reduce an arbitrary diagram to a Le-diagram. We give enumerative results and relate our Le-diagrams to other combinatorial objects. Surprisingly, the totally non-negative cells in the open Schubert cell of the odd and even orthogonal Grassmannians are (essentially) in bijection with preference functions and atomic preference functions respectively.
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185168
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, August 19, 2015 - 11:43:25 AM
Last modification on : Thursday, February 7, 2019 - 5:55:42 PM
Long-term archiving on: : Friday, November 20, 2015 - 10:34:44 AM

File

dmAJ0104.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01185168, version 1

Collections

Citation

Thomas Lam, Lauren Williams. Total positivity for cominuscule Grassmannians. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.39-51. ⟨hal-01185168⟩

Share

Metrics

Record views

63

Files downloads

878