Alladi Ramakrishnan Hall

Unique Factorization Of Tensor Products For Kac-Moody Algebras

R. Venkatesh

TIFR, Mumbai

We consider integrable, category O modules of indecomposable
symmetrizable Kac-Moody algebras and prove that unique factorization of
tensor products of irreducible modules holds in this category, up to
twisting by one dimensional modules. This generalizes a fundamental
theorem of Rajan for finite dimensional simple Lie algebras over C. Our
proof is new even for the finite dimensional case, and uses an interplay
of representation theory and combinatorics to analyze the Kac-Weyl
character formula. Further a new interpretation of the chromatic
polynomials of graphs is obtained using similar analysis.