Traces on diagram algebras II: centralizer algebras of easy groups and new variations of the Young graph
Algebraic Combinatorics, Volume 5 (2022) no. 3, pp. 413-436.

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

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DOI: 10.5802/alco.218
Classification: 20G42,  05E10,  05A18
Keywords: Branching graph, minimal boundary, trace simplex, easy quantum groups.
Wahl, Jonas 1

1 Hausdorff Center for Mathematics Endenicher Allee 62 D-53115 Bonn, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Wahl, Jonas. Traces on diagram algebras II:  centralizer algebras of easy groups and new variations of the Young graph. Algebraic Combinatorics, Volume 5 (2022) no. 3, pp. 413-436. doi : 10.5802/alco.218. https://alco.centre-mersenne.org/articles/10.5802/alco.218/

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