Traces on diagram algebras II: centralizer algebras of easy groups and new variations of the Young graph

In continuation of our recent work [39], we classify the extremal traces on infinite diagram algebras that appear in context Schur–Weyl duality for Banica and Speicher’s easy groups [3]. We show branching graphs these describe walks new variations Young graph which turn explicate curious ways growing diagrams. As a consequence, prove generic rook-Brauer are always extensions group algebra ℂ[S ∞ ] symmetric group. Moreover, conjecture same is true parameter deformations centralizers hyperoctahedral reduce this to conceptually much simpler numerical statement. Lastly, address trace classification problem dual halfliberated orthogonal O N * , case ×S ]. Our approach relies methods developed by Vershik Nikitin [37].