From the deformed Virasoro algebra to Temperley-Lieb algebras

Azat Gainutdinov (University of Hamburg)

Tuesday 4th February, 2014 15:00-16:00 Maths 326


Deformation of the infinite dimensional Lie algebra Virasoro resembles the well-known deformation of classical simple Lie algebras to quantum algebras. Such a deformation of the Virasoro algebra appeared to be useful in many applications to off-critical statistical models and massive integrable field theories. In the talk, I present my recent results on a surprising realization of this algebra in tensor products of N copies of the natural representation of the quantum group for sl(2). More formally, it turns out that the deformed Virasoro at N-th root of unity has representations realized by the Temperley-Lieb algebras with N generators. Such finite-dimensional representations are of the cyclic type (similar to those for quantum groups at roots of unity) and were never observed before. I will also discuss a limit when N goes to infinity.

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