arXiv math/00011142000-01-20math.QAmath.CO

Fermionic formulas for level-restricted generalized Kostka polynomials and coset branching functions

Anne Schilling, Mark Shimozono

备注：: 67 pages, axodraw style file needed
发表信息：: Commun.Math.Phys. 220 (2001) 105-164
DOI：: 10.1007/s002200100443

英文摘要：

Level-restricted paths play an important role in crystal theory. They correspond to certain highest weight vectors of modules of quantum affine algebras. We show that the recently established bijection between Littlewood--Richardson tableaux and rigged configurations is well-behaved with respect to level-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 fermionic formulas.

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