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arXiv · 1704.08048

Cluster algebras of finite type via a Coxeter element and Demazure Crystals of type B,C,D

Yuki Kanakubo
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Abstract

For a classical group $G$ and a Coxeter element $c$ of the Weyl group, it is known that the coordinate ring $\mathbb{C}[G^{e,c^2}]$ of the double Bruhat cell $G^{e,c^2}:=B\cap B_-c^2B_-$ has a structure of cluster algebra of finite type, where $B$ and $B_-$ are opposite Borel subgroups. In this article, we consider the case $G$ is of type ${\rm B}_r$, ${\rm C}_r$ or ${\rm D}_r$ and describe all the cluster variables in $\mathbb{C}[G^{e,c^2}]$ as monomial realizations of certain Demazure crystals.

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Yuki Kanakubo. 2017-04-26. Cluster algebras of finite type via a Coxeter element and Demazure Crystals of type B,C,D. https://arxiv.org/abs/1704.08048

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