Harmonic Analysis on the quantum Lorentz group

Details Harmonic Analysis on the quantum Lorentz group Harmonic Analysis on the quantum Lorentz group

1997-10-17

arxiv.org/abs/q-alg/9710022v2

Commun.Math.Phys. 207 (1999) 499-555

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

60 pages, tared gzipped Postscript file, major revision of the previous version, the Plancherel theorem is established in the

Scientific paper

10.1007/s002200050736

This work begins with a review of complexification and realification of Hopf algebras. We emphasize the notion of multiplier Hopf algebras for the description of different classes of functions (compact supported, bounded, unbounded) on complex quantum groups and the construction of the associated left and right Haar measure. Using a continuation of $6j$ symbols of $SU_q (2)$ with complex spins, we give a new description of the unitary representations of $SL_q (2,\CC)_{\RR}$ and find explicit expressions for the characters of $SL_q (2,\CC)_{\RR}$. The major theorem of this article is the Plancherel theorem for the Quantum Lorentz Group.

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