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arXiv · 0911.3553

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

Laurent Freidel·Etera R. Livine
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Abstract

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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Laurent Freidel, Etera R. Livine. 2009-11-18. The Fine Structure of SU(2) Intertwiners from U(N) Representations. https://doi.org/10.1063/1.3473786

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