On the relation between the modular double of U_q(sl(2,R)) and the quantum Teichmueller theory

2013/02/14 by I. Nidaiev, Nidaiev, I., J. Teschner +1
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1302.3454

40 pages, 30 figures

arxiv created 2013/02/14 · openalex publication_date 2013/02/14 · arxiv updated 2013/02/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We exhibit direct relations between the modular double of U_q(sl(2,R)) and the quantum Teichmueller theory. Explicit representations for the fusion- and braiding operations of the quantum Teichmueller theory are immediate consequences. Our results include a simplified derivation of the Clebsch-Gordan decomposition for the principal series of representation of the modular double of U_q(sl(2,R)).

Citations

• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• 6j Symbols for the Modular Double, Quantum Hyperbolic Geometry, and Supersymmetric Gauge Theories

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