Rigged configurations - a connection between physics and combinatorics

Anne Schilling

UC Davis

September 17,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

The aim of this talk is to give an introduction to rigged configurations. Rigged configurations were first introduced by Kerov, Kirillov and Reshetikhin in the 1980's in their study of the XXX model: rigged configurations are combinatorial objects which label the eigenvectors and eigenvalues of the XXX Hamiltonian obtained from the Bethe Ansatz. From the representation theoretic point of view, the XXX model can be described as a tensor product of GL_n representations. The number of eigenvectors should hence be equal to the number of highest weight elements. From the combinatorial point of view this correspondence is given by a bijection between rigged configurations and highest weight crystal paths. This bijection has many astonishing properties which we will discuss.

If time permits I will also mention a new rigged configuration bijection for type D.


Speaker's Contact Info: anne(at-sign)math.ucdavis.edu


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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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