by
Vyacheslav Spiridonov(BLTP JINR, Dubna and MPIM, Bonn)
→
Europe/Berlin
Seminar Room 2 (DESY, building 2a)
Seminar Room 2
DESY, building 2a
Description
Importance of the modular group in the consideration of quantum algebras and related structures was stressed by Faddeev in a 1994-1999 series of papers. The representation theory of the modular double of $U_q(sl_2)$ was systematically explored by Ponsot and Teschner in applications to the quantum Liouville model. We describe the elliptic modular double composed out of a pair of the Sklyanin algebras and outline the structure of its finite-dimensional representations leading to new elliptic solutions of the Yang-Baxter equation. There exists also the "hyperbolic modular double", an algebra lying "in between" the Faddeev and ellpitic modular doubles, which will be described as well.