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- W3105472523 abstract "We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a, b, h; p, q, r) that one usually associates with such a group and hence with a simply-laced Coxeter–Dynkin diagram have a meaningful definition for the non-simply-laced diagrams, too, and as a byproduct we extend Saito’s formula for the determinant of the Cartan matrix to all cases. Returning to invariant theory we show that for each irreducible representation i of a binary tetrahedral, octahedral, or icosahedral group one can find a homomorphism into a finite complex reflection group whose defining reflection representation restricts to i." @default.
- W3105472523 created "2020-11-23" @default.
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- W3105472523 date "2006-11-08" @default.
- W3105472523 modified "2023-09-27" @default.
- W3105472523 title "Quantum affine Cartan matrices, Poincaré series of binary polyhedral groups, and reflection representations" @default.
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- W3105472523 doi "https://doi.org/10.1007/s00229-006-0055-1" @default.
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