**R. Venkatesh**

TIFR

July 25, 2013

**Chromatic polynomials of graphs from Kac-Moody algebras**:
There is a natural way of associating a symmetrizable Kac-Moody
algebra $g$ with the given simple graph G: $g$ is the Kac-Moody algebra constructed from the generalized Cartan matrix 2I-A, where A is the adjacency matrix of G. We give a new interpretation of the chromatic polynomial of G in terms of the Kac-Moody Lie algebra $g$. More preciously, we show that the chromatic polynomial of G is essentially the q-Kostant partition function of $g$ evaluated on the sum of the simple roots.