Total positivity for cominuscule Grassmannians

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Total positivity for cominuscule Grassmannians

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Title: Total positivity for cominuscule Grassmannians
Author: Williams, Lauren; Lam, Thomas

Note: Order does not necessarily reflect citation order of authors.

Citation: Lam, Thomas, and Lauren Williams. 2008. Total positivity for cominuscule Grassmannians. New York Journal of Mathematics 14.
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Abstract: In this paper we explore the combinatorics of the non-negative part (G/P)+ 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)+. 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.
Other Sources: http://arxiv.org/abs/0710.2932
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2796935

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  • FAS Scholarly Articles [7219]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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