Root Multiplicities of the Kac-Moody Algebras HA(1)n Original Research Article

We give a root multiplicity formula for all the roots of almost hyperbolic Kac-Moody algebras HA(1)n. We use the path realization of crystal bases for the irreducible highest weight modules over quantum affine Lie algebras Uq(A(1)n) to determine the root multiplicities.