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The hive model and the polynomial nature of stretched Littlewood-Richardson coefficients. (English) Zbl 1178.05100

Summary: The hive model is used to explore the properties of both ordinary and stretched Littlewood-Richardson coefficients. The latter are polynomials in the stretching parameter \(t\). It is shown that these may factorise, and that they can then be expressed as products of certain primitive polynomials. It is further shown how to determine a sequence of linear factors \((t+m)\) of the primitive polynomials, as well as bounds on their degree which are conjectured to be exact.

MSC:

05E10 Combinatorial aspects of representation theory
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