Seminar

The Yangian Yg and quantum loop algebra Uq(Lg) of a complex semisimple Lie algebra g are infinite-dimensional quantum groups which were introduced by Drinfeld in the mid 80s, and deform the current algebra g[s] and loop algebra g[z,z^{-1}] of g.

Although they share very many similarities, and were long thought to have the same representations, no precise relation between them existed until recently.

I will explain how to construct a faithful functor from the finite-dimensional representations of Yg to those of Uq(Lg) which restricts to an equivalence on an explicitly defined subcategory of Yg.

A similar construction yields a faithful functor from representations of U_q(Lg) to those of the elliptic quantum group corresponding to g.

This is joint work with Sachin Gautam.

(no prior knowledge of Yg and Uq(Lg) will be assumed)