Inductive limits of compact quantum groups and their unitary representations

We introduce inductive limits of compact quantum groups and their unitary representation theories. Those give a more explicit representation-theoretic meaning to our previous study quantization characters central probability measures in the asymptotic theory. also tensor product representations infinite-dimensional group. As by-product, we an interpretation certain transformations that play important role analyzing q-central on paths q-Gelfand–Tsetlin graph.