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March 2017 Explicit Forms of Cluster Variables on Double Bruhat Cells $G^{u,e}$ of Type C
Yuki KANAKUBO, Toshiki NAKASHIMA
Tokyo J. Math. 39(3): 643-678 (March 2017). DOI: 10.3836/tjm/1475723089

Abstract

Let $G=Sp_{2r}({\mathbb C})$ be a simply connected simple algebraic group over $\mathbb{C}$ of type $C_r$, $B$ and $B_-$ its two opposite Borel subgroups, and $W$ the associated Weyl group. For $u$, $v\in W$, it is known that the coordinate ring ${\mathbb C}[G^{u,v}]$ of the double Bruhat cell $G^{u,v}=BuB\cup B_-vB_-$ is isomorphic to an upper cluster algebra $\overline{\mathcal{A}}(\textbf{i})_{{\mathbb C}}$ and the generalized minors $\Delta(k;\textbf{i})$ are the cluster variables of ${\mathbb C}[G^{u,v}]${5}. In the case $v=e$, we shall describe the generalized minor $\Delta(k;\textbf{i})$ explicitly.

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Yuki KANAKUBO. Toshiki NAKASHIMA. "Explicit Forms of Cluster Variables on Double Bruhat Cells $G^{u,e}$ of Type C." Tokyo J. Math. 39 (3) 643 - 678, March 2017. https://doi.org/10.3836/tjm/1475723089

Information

Published: March 2017
First available in Project Euclid: 6 October 2016

zbMATH: 1378.13013
MathSciNet: MR3634287
Digital Object Identifier: 10.3836/tjm/1475723089

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.39 • No. 3 • March 2017
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