330 research outputs found
Examples of weakly amenable discrete quantum groups
We prove that Wang's free orthogonal and free unitary quantum groups are
weakly amenable and that their Cowling-Haagerup constant is equal to 1. This is
achieved by estimating the completely bounded norm of the projections on the
coefficients of irreducible representations of their compact duals. An argument
of monoidal equivalence then allows us to extend this result to quantum
automorphism groups of finite spaces and even yields some examples of weakly
amenable non-unimodular discrete quantum groups with the Haagerup property.Comment: 25 page
Permanence of approximation properties for discrete quantum groups
We prove several results on the permanence of weak amenability and the
Haagerup property for discrete quantum groups. In particular, we improve known
facts on free products by allowing amalgamation over a finite quantum subgroup.
We also define a notion of relative amenability for discrete quantum groups and
link it with amenable equivalence of von Neumann algebras, giving additional
permanence properties.Comment: 18 pages, Ann. Inst. Fourier (2014
The radial MASA in free orthogonal quantum groups
We prove that the radial subalgebra in free orthogonal quantum group factors
is maximal abelian and mixing, and we compute the associated bimodule. The
proof relies on new properties of the Jones-Wenzl projections and on an
estimate of certain scalar products of coefficients of irreducible
representations.Comment: 20 pages ; v2 : minor improvement
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