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Schur Polynomials and the Yang-Baxter equation


Speaker: Dan Bump, Stanford
Location: 1147 MSB
Start time: Mon, Jan 25 2010, 4:10PM

The six-vertex model is one of the best known exactly solved models in statistical physics. It has interesting applications outside of physics, and was one of the motivating examples in the development of quantum groups. One considers a lattice in the plane. A state of the system is an assignment of signs to the edges of the lattice. One evaluates the state by multiplying certain ``Boltzmann weights'' over the vertices of the lattice. Summing over all possible states of the system gives the partition function. Miraculously, this can be exactly computed. One method of doing this, due to Baxter, involves the so-called Yang-Baxter equation. We will show that in the so-called fermionic case, where the Boltzmann weights create a system that is as disordered as possible, there is a parametrized Yang-Baxter equation with nonabelian parameter group GL(2)xGL(1). As an application, we will see that the weights may be chosen so that the partition function is a Schur polynomial times a deformation of the Weyl denominator. This gives new proofs of results of Tokuyama and of Hamel and King, which are deformations of the Weyl character formula. This is joint work with Brubaker and Friedberg. See:

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