Littlewood-Richardson Coeffients via Yang-Baxter Equations
refreshments at 3:45pm
The purpose of this talk is to present a combinatorial interpretation for the
decomposition of the tensor product of two or more irreducible representations
of GL(n) in terms of certain scattering R-matrix. This R-matrix satisfies a
Yang-Baxter type equation. The corresponding piecewise-linear transformation
of parameters maps coincide with the transition maps for Kashiwara
parametrizations of canonical bases for modules over type A quantum groups.
We provide an explicit description for the cone of such parameterizations, thus
solving a problem posed by Berenstein and Zelevinsky. Geometrically, our
R-matrix can be interpreted via certain web diagrams, which are similar in
appearance to honeycomb tinkertoys of Knutson and Tao.
This is a joint work with Oleg Gleizer.
Speaker's Contact Info: apost at math.mit.edu
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