Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
McKay Centralizer Algebras
Georgia Benkart  1  , Tom Halverson  2  
1 : Department of Mathematics [Madison]  -  Website
480 N Lincoln Dr., Madison, WI 53706 -  États-Unis
2 : Department of Mathematics, Statistics, and Computer Science [Saint-Paul]  -  Website
Macalester College, Olin-Rice Science Center, Room 222 Saint Paul, MN -  États-Unis

For a finite subgroup G of the special unitary group SU2, we study the centralizer algebra Zk(G) = EndG(Vk) 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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