Cluster algebras of finite type via Coxeter elements and principal minors
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in the simply connected semisimple algebraic group of the same Cartan-Killing type. In this realization, the cluster variables appear as certain (generalized) principal minors.
38 pages, 2 figures; v2: minor editorial changes, to appear in Transformation Groups
38 pages, 2 figures; v2: minor editorial changes, to appear in Transformation Groups