Quantization of branching coefficients for classical Lie groups
arXiv:math/0602089
Abstract
We study natural quantizations of branching coefficients corresponding to the restrictions of the classical Lie groups to their Levi subgroups. We show that they admit a stable limit which can be regarded as a -analogue of a tensor product multiplicity. According to a conjecture by Shimozono, the stable one-dimensional sum for nonexceptional affine crystals are expected to occur as special cases of these -analogues.