I will talk about the construction of the continuous series of affine
sl(2,R), based on the representation theory of loop ax+b group. Possible
relations with modular double representations of U_q(sl(2,R)) will be also
discussed.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/158