Factorization rules in quantum Teichmuller theory.

摘要

For a punctured surface S, a point of its Teichmuller space T (S) determines an irreducible representation of its quantization Tq (S). We analyze the behavior of these representations as one goes to infinity in T (S), or in the moduli space M (S) of the surface. Our main result states that an irreducible representation of Tq (S) tend in an appropriate sense to a direct sum of representations of Tq (Sgamma), where Sgamma is obtained from S by pinching a multicurve gamma to a set of nodes. The result is analogous to the factorization rule found in conformal field theory.