  This article focuses on two related topics: unitary representations of the
loop $ax+b$-group and their relation to a loop version of the $\Gamma$-function
and the construction of continuous series for the
$\widehat{sl(2,\mathbb{R})}$-algebra. Mainly this is a survey of some results
from arXiv:1012.4826 , arXiv:1210.2135 alongside with the motivation for them
both from the physical and mathematical points of view.
