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### Extremal loop weight representations of quantum toroidal algebras

**Algebra & Discrete Mathematics**

Speaker: | Mathieu Mansuy, Institut de Mathematiques de Jussieu |

Location: | 3106 MSB |

Start time: | Fri, Jan 10 2014, 5:10PM |

We give different constructions of new integrable representations of quantum toroidal algebras (double affinization of quantum groups), called extremal loop weight representations. Its definition is given by Hernandez in 2009, following the one of extremal weight representations for quantum affine algebras given by Kashiwara. The aim, like in the works of Kashiwara, is to construct finite-dimensional representations of the quantum toroidal algebras, but at roots of unity in this case.

This talk will be aimed at graduate students!

This talk is also part of MAT 280 on "Macdonald polynomials and crystal bases".