Fermionic formulas for level-restricted generalized Kostka polynomials andcoset branching functions

Level-restricted paths play an important role in crystal theory. They corre spond to certain highest weight vectors of modules of quantum affine algebr as. We show that the recently established bijection between Littlewood-Rich ardson tableaux and rigged configurations is well-behaved with respect to l evel-restriction and give an explicit characterization of level-restricted rigged configurations. As a consequence a new general fermionic formula for the level-restricted generalized Kostka polynomial is obtained. Some coset branching functions of type A are computed by taking limits of these fermi onic formulas.