Cartan matrix
Let be a reduced root system, with a Euclidean vector space, with inner product , and let be a base of this root system. Then the Cartan matrix of the root system is the matrix
The Cartan matrix uniquely determines the root system, and is unique up to simultaneous permutation of the rows and columns. It is also the basis change matrix from the basis of fundamental weights to the basis of simple roots in .
Title | Cartan matrix |
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Canonical name | CartanMatrix |
Date of creation | 2013-03-22 13:17:56 |
Last modified on | 2013-03-22 13:17:56 |
Owner | bwebste (988) |
Last modified by | bwebste (988) |
Numerical id | 4 |
Author | bwebste (988) |
Entry type | Definition |
Classification | msc 17B20 |