Liouville model, Euler factors and constant term identities

Some similar integrals appeared independently in two seamingly different areas:
in a study of automorphic L-functions on the one hand and in physicists’ works
on the Liouville model of 2D Conformal field theory and on Chern - Simons
theory on the other.  We will discuss relationships between the two domains, as
well as further connections with Dyson - Macdonald constant term identities.
This is a joint work with Bui Van Binh.