A simplified Kronecker rule for one hook shape

Abstract

Recently Blasiak has given a combinatorial rule for the Kronecker coefficient g λ μ ν g_{\lambda \mu \nu } when μ \mu is a hook shape by defining a set of colored Yamanouchi tableaux with cardinality g λ μ ν g_{\lambda \mu \nu } 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.