Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 6 (2013), 3411-3446.
Factorization rules in quantum Teichmüller theory
For a punctured surface , a point of its Teichmüller space determines an irreducible representation of its quantization . We analyze the behavior of these representations as one goes to infinity in , or in the moduli space of the surface. The main result of this paper states that an irreducible representation of limits to a direct sum of representations of , where is obtained from by pinching a multicurve to a set of nodes. The result is analogous to the factorization rule found in conformal field theory.
Algebr. Geom. Topol., Volume 13, Number 6 (2013), 3411-3446.
Received: 8 February 2013
Accepted: 19 April 2013
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 20G42: Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
Roger, Julien. Factorization rules in quantum Teichmüller theory. Algebr. Geom. Topol. 13 (2013), no. 6, 3411--3446. doi:10.2140/agt.2013.13.3411. https://projecteuclid.org/euclid.agt/1513715737