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Article Dans Une Revue Journal of Functional Analysis Année : 2005

Quantum automorphism groups of homogeneous graphs

Résumé

Associated to a finite graph $X$ is its quantum automorphism group $G$. The main problem is to compute the Poincar\\é series of $G$, meaning the series $f(z)=1+c_1z+c_2z^2+...$ whose coefficients are multiplicities of 1 into tensor powers of the fundamental representation. In this paper we find a duality between certain quantum groups and planar algebras, which leads to a planar algebra formulation of the problem. Together with some other results, this gives $f$ for all homogeneous graphs having 8 vertices or less.

Dates et versions

hal-00012813 , version 1 (27-10-2005)

Identifiants

Citer

Teodor Banica. Quantum automorphism groups of homogeneous graphs. Journal of Functional Analysis, 2005, 224, no.2, pp.243-280. ⟨hal-00012813⟩
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