A simplified Kronecker rule for one hook shape

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...

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Published in:Proceedings of the American Mathematical Society 2017-09, Vol.145 (9), p.3657-3664
Main Author: LIU, RICKY INI
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Language:English
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A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
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description 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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subjects A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
title A simplified Kronecker rule for one hook shape
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