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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2020

McKay Centralizer Algebras

Résumé

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.
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Dates et versions

hal-02173744 , version 1 (04-07-2019)

Identifiants

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Georgia Benkart, Tom Halverson. McKay Centralizer Algebras. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6360⟩. ⟨hal-02173744⟩

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