Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations
| dc.creator | Suter, Ruedi | |
| dc.date | 2005-03-24 | |
| dc.date.accessioned | 2026-07-07T07:36:35Z | |
| dc.date.available | 2026-07-07T07:36:35Z | |
| dc.description | 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. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503542 | |
| dc.identifier | http://arxiv.org/abs/math/0503542 | |
| dc.identifier | Manuscripta mathematica 122 (2007), no. 1, 1-21 | |
| dc.identifier | doi:10.1007/s00229-006-0055-1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120478 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C15; 13A50; 20F55; 22E40 | |
| dc.title | Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations | |
| dc.type | text |