Abstract
We study the root multiplicities of the indefinite Kac–Moody algebras by viewing them as weight multiplicities of certain integrable
-modules. Then using Kang's root multiplicity formula and the path crystal for integrable
-modules we calculate the multiplicities of a family of roots for
. In particular, we show that for any positive integer k the multiplicity of − 2α−1 − kδ as a root of
is a polynomial in n of degree at most k. Furthermore, we observe that Frenkel's conjectured root multiplicity bound does not hold for roots of
.
ACKNOWLEDGMENT
This article is partially supported by NSA grant MDA904-02-1-0072.
Notes
Communicated by J. Kuzmanovich.