Function theory on a qq-analog of complex hyperbolic space

This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on ‘finite’ functions on a quantum hyperbolic space and on the associated quantum isotropic cone. Also we establish principal series of Uqsun,mUqsun,m-modules related to this cone, and obtain the necessary conditions for those modules to be equivalent.

► Basic notions of function theory on quantum complex hyperbolic spaces are expounded.
► Principal series of modules related to the associated isotropic cone is established.
► The necessary conditions for those modules to be equivalent are obtained.
► Pricipal unitary series of Uqsln,mUqsln,m-modules is found.