Grassmannians and cluster algebras

• Autores: S. Scott
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 92, Nº 2, 2006, págs. 345-380
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • This paper follows the program of study initiated by S. Fomin and A. Zelevinsky, and demonstrates that the homogeneous coordinate ring of the Grassmannian $\mathbb{G}(k, n)$ is a {\it cluster algebra of geometric type}. Those Grassmannians that are of {\it finite cluster type} are identified and their cluster variables are interpreted geometrically in terms of configurations of points in $\mathbb{C}\mathbb{P}^2$.