Bosonic formula for level-restricted paths

Abstract

We prove a bosonic formula for the generating function of level-restricted paths for the infinite families of affine Kac-Moody algebras. In affine type A this yields an expression for the level-restricted generalized Kostka polynomials.

16 pages, AMS-LaTeX, style file axodraw.sty required; Lemma 4 extended to include perfect crystals of level 2