Sachin Gautam, Columbia University
“Elliptic quantum groups”
In 1995 G. Felder introduced an elliptic Rmatrix, which satisfies a dynamical version of the YangBaxter equation. The elliptic quantum group of sl(n) is then defined in the same vein as the usual Rmatrices give rise to quantum groups via the RTT formalism of Faddeev, Reshetikhin and Takhtajan.
In this talk I will explain Felders definition and generalize it to the case of arbitrary Kac- Moody Lie algebras analogous to Drinfelds new presentation of Yangians and quantum loop algebras. I will also present a method of constructing representations of the elliptic quan- tum group using qdifference equations. In particular, we classify irreducible representations of the elliptic quantum group, which is reminiscent of Drinfelds classification of irreducible representations of Yangians.
This talk is based on a joint work with V. Toledano Laredo.
MC 5413