Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U(q)(sl(2,R))

Ponsot, B.; Teschner, J.

doi:10.1007/PL00005590

Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U(q)(sl(2,R))

B. Ponsot
(
- Montpellier U.
)
,
J. Teschner
(
- Freie U., Berlin
)

Jul, 2000

39 pages

Published in:

Commun.Math.Phys. 224 (2001) 613-655

e-Print:

math/0007097 [math.QA]

DOI:

10.1007/PL00005590

Report number:

DIAS-STP-00-15,
BERLIN-SFB-288,
LPM-00-21

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Abstract:

The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of

U_q(sl(2,R)

. It is described by an explicit integral transformation involving a distributional kernel that can be seen as an analogue of the Clebsch-Gordan coefficients. Moreover, we also study the relation between two canonical decompositions of triple tensor products into irreducibles. It can be represented by an integral transformation with a kernel that generalizes the Racah-Wigner coefficients. This kernel is explicitly calculated.

Note:

39 pages, AMS-Latex; V2: Added comments and references concerning relation to Faddeev's modular double, minor corrections, version to be published in CMP Subj-class: Quantum Algebra

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