Geometric crystals and cluster ensembles in Kac-Moody setting

DOI10.1016/j.geomphys.2019.103576zbMath1442.13074arXiv1807.11684OpenAlexW2994726764WikidataQ126563636 ScholiaQ126563636MaRDI QIDQ2302556

Toshiki Nakashima, Yuki Kanakubo

Publication date: 26 February 2020

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.11684

zbMATH Keywords

crystalsdouble Bruhat cellscluster ensemblesgeometric crystals

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Kac-Moody groups (20G44) Cluster algebras (13F60)

Cites Work

• Decorations on geometric crystals and monomial realizations of crystal bases for classical groups
• Geometric crystals on Schubert varieties
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• The crystal base and Littelmann's refined Demazure character formula
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• Kac-Moody groups, their flag varieties and representation theory
• Cluster ensembles and Kac-Moody groups
• Canonical bases for cluster algebras
• Birational geometry of cluster algebras
• Twist Automorphisms on Quantum Unipotent Cells and Dual Canonical Bases
• Cluster ensembles, quantization and the dilogarithm
• Infinite flag varieties and conjugacy theorems
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