Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Benkart Georgia

Tuesday 5
Combinatorics
Eric Fusy
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
McKay Centralizer Algebras
Georgia Benkart  1  , Tom Halverson  2  
1 : University of Wisconsin-Madison [Madison]  -  Website
Madison, WI 53706 -  États-Unis
2 : Macalester College
Saint Paul, MN 55105 -  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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