  Recently a quantum group deformation of EPRL spinfoam model was proposed in
arXiv:1012.4216 by one of the authors, and in arXiv:1012.4784 by Fairbairn and
Meusburger. It is interesting to study the high spin asymptotics of the quantum
group spinfoam model, to see if it gives the discrete Einstein gravity with
cosmological constant as its semiclassical limit. In this article we propose a
new technique, which can simplify the analysis of the high spin asymptotics for
quantum group spinfoam vertex amplitude. This technique can generalize the
spinfoam asymptotic analysis developed by Barrett, et al to quantum group
spinfoam. As a preparation of asymptotic analysis, we define and analyze the
coherent states and coherent intertwiners for quantum group, which has certain
"factorization properties". We show that in the high spin limit of quantum
group spinfoam, many q-deformed noncommutative ingredients become classical and
commutative. In particular, the squared norm of coherent intertwiner and the
(Euclidean) vertex amplitude become integrals on classical group, while there
are some additional terms (written in terms of classical group variables) make
quantum group corrections to the usual (classical group) coherent intertwiner
and vertex amplitude. These quantum group correction terms turn out to be
proportional to the deformation parameter, which hopefully gives the
cosmological term as its semiclassical limit.
