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The Fine Structure of SU(2) Intertwiners from U(N) Representations

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arxiv 0911.3553 v1 pith:XKFSR7CA submitted 2009-11-18 gr-qc math-phmath.MP

Laurent Freidel , Etera R. Livine This is my paper · ORCID
classification gr-qcmath-phmath.MP
keywords spaceareafixedgrouphilbertintertwinerstotalblack
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In this work we study the Hilbert space space of N-valent SU(2) intertwiners with fixed total spin, which can be identified, at the classical level, with a space of convex polyhedra with N face and fixed total boundary area. We show that this Hilbert space provides, quite remarkably, an irreducible representation of the U(N) group. This gives us therefore a precise identification of U(N) as a group of area preserving diffeomorphism of polyhedral spheres. We use this results to get new closed formulae for the black hole entropy in loop quantum gravity.

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  1. Homothetic expansion of polyhedra in the two-vertex model: emergence of FLRW

    gr-qc 2025-07 conditional novelty 6.0 of 10

    In the U(N)-symmetric sector of the two-vertex loop-quantum-gravity model, the face frames of the twisted-geometry polyhedra evolve by a common scaling plus rotation, so all planar angles stay constant and the polyhed...

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