Quantization of branching coefficients for classical Lie groups

Details Quantization of branching coefficients for classical Lie groups Quantization of branching coefficients for classical Lie groups

2006-02-06

arxiv.org/abs/math/0602089v1

Mathematics

Representation Theory

Scientific paper

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 $q$-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 $q$-analogues.

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