6j symbols for U_q(sl₂) and non-Euclidean tetrahedra

2003/05/07 by Yuka U. Taylor, Taylor, Yuka U., Christopher T. Woodward +1
Mathematics · #20G42 (53D50) #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math.QA #math.SG #msc:20G42

paper · pdf · doi:10.48550/arxiv.math/0305113

34 pages. Rewritten. To appear in Selecta Math

openalex publication_date 2003/05/07 · arxiv created 2005/05/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We relate the semiclassical asymptotics of the 6j symbols for the representation theory of the quantized enveloping algebra U_q(sl₂) at q a primitive root of unity, or q positive real, to the geometry of non-Euclidean tetrahedra. The formulas are motivated by the geometry of conformal blocks in the Wess-Zumino-Witten model; they generalize formulas in the case q = 1 of Wigner, Ponzano and Regge, and Schulten and Gordon, proved by J. Roberts.

Citations

• Invariants of links with flat connections in their complements.II. Holonomy R-matrices related to quantized universal enveloping algebras at roots of 1

Related

• Asymptotics and 6j-symbols
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
• Asymptotics of b-6j symbols and anti-de Sitter tetrahedra
• Asymptotics of quantum 6j symbols
• Asymptotics of quantum 6j-symbols and generalized hyperbolic tetrahedra