A SIMPLIFIED KRONECKER RULE FOR ONE HOOK SHAPE

摘要

Recently Blasiak has given a combinatorial rule for the Kronecker coefficient g lambda mu v when mu is a hook shape by defining a set of colored Yamanouchi tableaux with cardinality g lambda mu v in terms of a process called conversion. We give a characterization of colored Yamanouchi tableaux that does not rely on conversion, which leads to a simpler formulation and proof of the Kronecker rule for one hook shape.