2005/03/31 by Teodor Banica, Julien Bichon · 2 citations
Mathematics · #math.QA #msc:16W30
published as J. Inst. Math. Jussieu 6 (2007), 381-414 · 31 pages
arxiv created 2006/03/01 · arxiv updated 2009/12/01
Associated to a finite graph X is its quantum automorphism group G(X). We prove a formula of type G(X*Y)=G(X)*wG(Y), where *w is a free wreath product. Then we discuss representation theory of free wreath products, with the conjectural formula μ(G*wH)=μ(G)\boxtimesμ(H), where μ is the associated spectral measure. This is verified in two situations: one using free probability techniques, the other one using planar algebras.