Topological representations of \(U_ q(\text{sl}_ 2(\mathbb{C}))\) on the torus and the mapping class group

DOI10.1007/BF00761424zbMath0828.57010arXivhep-th/9307188MaRDI QIDQ1314810

M. Crivelli, Giovanni Felder, Christian Wieczerkowski

Publication date: 7 January 1996

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9307188

zbMATH Keywords

quantum groupsmapping class groupconformal field theories on the torusspace of holomorphic multivalued differential formstopological representations of \(U_ q\text{sl}_ 2 (\mathbb{C})\)torus with one puncture

Mathematics Subject Classification ID

Covering spaces and low-dimensional topology (57M10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40)

Related Items

Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity, Elliptic KZ system, braid group of the torus and Vassiliev invariants

Cites Work

• Modular covariance of minimal model correlation functions
• Quantum groups, quantum categories and quantum field theory
• SU(2) Chern-Simons theory at genus zero
• Topological representations of the quantum group \(U_ q(sl_ 2)\)
• Fock representations and BRST cohomology in \(\mathrm{SL}(2)\) current algebra
• Infinite conformal symmetry in two-dimensional quantum field theory
• Arrangements of hyperplanes and Lie algebra homology
• Generalized hypergeometric functions on the torus and the adjoint representation of \(U_ q(sl_ 2)\)
• Invariants of 3-manifolds via link polynomials and quantum groups
• A TOPOLOGICAL APPROACH TO REPRESENTATIONS OF THE IWAHORI-HECKE ALGEBRA
• Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras