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Toric degenerations of integrable systems on Grassmannians and polygon spaces

Published online by Cambridge University Press:  11 January 2016

Yuichi Nohara  and
Kazushi Ueda
Yuichi Nohara
Affiliation:
Yuichi Nohara Faculty of Education Kagawa University TakamatsuKagawa 760-8522Japannohara@ed.kagawa-u.ac.jp
Kazushi Ueda
Affiliation:
Department of Mathematics Graduate School of Science Osaka UniversityToyonaka Osaka, 560-0043Japankazushi@math.sci.osaka-u.ac.jp
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Abstract

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We introduce a completely integrable system on the Grassmannian of 2-planes in an n-space associated with any triangulation of a polygon with n sides, and we compute the potential function for its Lagrangian torus fiber. The moment polytopes of this system for different triangulations are related by an integral piecewise-linear transformation, and the corresponding potential functions are related by its geometric lift in the sense of Berenstein and Zelevinsky.

Keywords

37J3553D37
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 214 , June 2014 , pp. 125 - 168
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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