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Toric matrix Schubert varieties and their polytopes


Authors: Laura Escobar and Karola Mészáros
Journal: Proc. Amer. Math. Soc. 144 (2016), 5081-5096
MSC (2010): Primary 14M25, 52B11, 05E45
DOI: https://doi.org/10.1090/proc/13152
Published electronically: May 23, 2016
MathSciNet review: 3556254
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Abstract: Given a matrix Schubert variety $ \overline {X_\pi }$, it can be written as $ \overline {X_\pi }=Y_\pi \times \mathbb{C}^q$ (where $ q$ is maximal possible). We characterize when $ Y_{\pi }$ is toric (with respect to a $ (\mathbb{C}^*)^{2n-1}$-action) and study the associated polytope $ \Phi (\mathbb{P}(Y_\pi ))$ of its projectivization. We construct regular triangulations of $ \Phi (\mathbb{P}(Y_\pi ))$ which we show are geometric realizations of a family of subword complexes. Subword complexes were introduced by Knutson and Miller in 2004, who also showed that they are homeomorphic to balls or spheres and raised the question of their polytopal realizations.


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Additional Information

Laura Escobar
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaigh, Urbana, Illinois 61801
Email: lescobar@illinois.edu

Karola Mészáros
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: karola@math.cornell.edu

DOI: https://doi.org/10.1090/proc/13152
Received by editor(s): August 23, 2015
Received by editor(s) in revised form: February 9, 2016
Published electronically: May 23, 2016
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2016 Laura Escobar and Karola Mészároz

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