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A simplified Kronecker rule for one hook shape


Author: Ricky Ini Liu
Journal: Proc. Amer. Math. Soc. 145 (2017), 3657-3664
MSC (2010): Primary 05E10; Secondary 20C30
DOI: https://doi.org/10.1090/proc/13692
Published electronically: May 24, 2017
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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.


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Ricky Ini Liu
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
Email: riliu@ncsu.edu

DOI: https://doi.org/10.1090/proc/13692
Received by editor(s): August 3, 2015
Published electronically: May 24, 2017
Communicated by: Harm Derksen
Article copyright: © Copyright 2017 American Mathematical Society