A simplified Kronecker rule for one hook shape

Abstract:

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