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

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

2009-11-18

arxiv.org/abs/0911.3553v1

J.Math.Phys.51:082502,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages

Scientific paper

10.1063/1.3473786

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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