Discrete quantum gravity the Lorentz invariant weight for th(6)

In a recent paper [1] we have constructed the spin and tensor representations of SO(4) from which the invariant weight can be derived for the Barrett-Crane model in quantum gravity. By analogy with the SO(4) group, we present the complexified Clebsch-Gorda

[3]NikiforovAF,SuslovSKandUvarovVB1991“ClassicalOrthogonalPolynomialsofaDiscrete

Variable”274–278(Springer).[4]GodementR1952Trans.Am.Math.Soc.73496–556“ATheoryofsphericalfunctions”.[5]CraneL,P´erezAandRovelliC“A nitenessprooffortheLorentzianstatesumspinfoammodel

forquantumgeneralrelativity”gr-qc/0104057.

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