14
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          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.

          Related collections

          Author and article information

          Journal
          24 March 2005
          Article
          10.1007/s00229-006-0055-1
          math/0503542
          9edc571b-5884-4880-b688-544713e47e70
          History
          Custom metadata
          20C15; 13A50; 20F55; 22E40
          Manuscripta mathematica 122 (2007), no. 1, 1-21
          19 pages
          math.RT

          Comments

          Comment on this article