TY - JOUR
AU1 - Barnes, Jeffrey M.
AU2 - Benkart, Georgia
AU3 - Halverson, Tom
AB - 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. These subgroups are in bijection with the simply laced affine Dynkin diagrams. The McKay correspondence relates the representation theory of these groups to the associated Dynkin diagram, and we use this connection to show that the structure and representation theory of Zk(G) as a semisimple algebra is controlled by the combinatorics of the corresponding Dynkin diagram.
TI - McKay centralizer algebras
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/pdv075
DA - 2016-02-01
UR - https://www.deepdyve.com/lp/wiley/mckay-centralizer-algebras-LLbOQ4aimN
SP - 375
EP - 414
VL - 112
IS - 2
DP - DeepDyve
ER -