Geodesic
McKay Centralizer Algebras
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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For a finite subgroup G of the special unitary group SU2, we study the centralizer algebra Zk(G) = EndG(V⊗k) of G acting on the k-fold tensor product of its defining representation V = C2. The McKay corre- spondence relates the representation theory of these groups to an associated affine Dynkin diagram, and we use this connection to study the structure and representation theory of Zk(G) via the combinatorics of the Dynkin diagram. When G equals the binary tetrahedral, octahedral, or icosahedral group, we exhibit remarkable connections between Zk (G) and the Martin-Jones set partition algebras. 
@article{DMTCS_2020_special_379_a42,
     author = {Benkart, Georgia and Halverson, Tom},
     title = {McKay {Centralizer} {Algebras}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6360},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6360/}
}
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Benkart, Georgia; Halverson, Tom. McKay Centralizer Algebras. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6360. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6360/

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