Given a simple graph G, the Kac-Moody Lie algebra of G is the Kac-Moody algebra whose simply laced Dynkin diagram is G. We give a new interpretation of the chromatic polynomial of G in terms of the Kac-Moody Lie algebra of G. We show that the chromatic polynomial is essentially th= e q-Kostant partition function of the associated Kac-Moody algebra evaluate= d on the sum of the simple roots. As an application, we construct basis of some of the root spaces of the Kac-Moody algebra of G. This is a joint work with Sankaran Viswanath.

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Last updated: 17 May 2024