6j symbols for U_q(sl_2) and non-Euclidean tetrahedra

Details 6j symbols for U_q(sl_2) and non-Euclidean tetrahedra 6j symbols for U_q(sl_2) and non-Euclidean tetrahedra

2003-05-07

arxiv.org/abs/math/0305113v3

Mathematics

Quantum Algebra

34 pages. Rewritten. To appear in Selecta Math

Scientific paper

We relate the semiclassical asymptotics of the 6j symbols for the representation theory of the quantized enveloping algebra U_q(sl_2) 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.

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