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GRASSMANNIANS AND CLUSTER ALGEBRAS

Published online by Cambridge University Press:  20 February 2006

JOSHUA S. SCOTT
JOSHUA S. SCOTT
Affiliation:
Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdomjs262@mcs.le.ac.uk
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Abstract

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 $\mathbb{C}\mathbb{P}^2$.

Keywords

22E4605Exx
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 92 , Issue 2 , March 2006 , pp. 345 - 380
Copyright
2006 London Mathematical Society

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