Georgia Benkart ; Tom Halverson - McKay Centralizer Algebras

dmtcs:6360 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6360
McKay Centralizer AlgebrasArticle

Authors: Georgia Benkart 1; Tom Halverson 2

  • 1 Department of Mathematics [Madison]
  • 2 Department of Mathematics, Statistics, and Computer Science [Saint-Paul]

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.

https://doi.org/10.46298/dmtcs.6360
Source: HAL:hal-02173744v1
Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • RUI: Combinatorics and Repesentations of Diagram Algebras; Funder: National Science Foundation; Code: 0800085
  • RootDetect: Remote Detection and Precision Management of Root Health; Funder: National Science Foundation; Code: 53706

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