Racah operators for principal series of representations of the group $\mathrm {SL}(2,\mathbb C)$

As a generalization of the well-known Racah coefficients (which are usually defined for finite-dimensional representations of semisimple Lie groups), the concept of Racah operators is introduced for locally compact groups with a ‘nice’ dual space. Explicit expressions for these operators are presented for $\operatorname{PSL}(2,\mathbb C)$.
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