McKay Centralizer Algebras

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 dia...

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Vydané v:	Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavní autori:	Benkart, Georgia, Halverson, Tom
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	DMTCS 22.04.2020 Discrete Mathematics & Theoretical Computer Science
Predmet:	[math.math-co]mathematics [math]/combinatorics [math.co] Combinatorics Mathematics
ISSN:	1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí:	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.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.6360