McKay trees

Avraham Aizenbud, Inna Entova-Aizenbud

Research output: Working paper/PreprintPreprint

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Given a finite group G and its representation ρ , the corresponding McKay graph is a graph Γ(G,ρ) whose vertices are the irreducible representations of G ; the number of edges between two vertices π,τ of Γ(G,ρ) is dimHomG(π⊗ρ,τ) . The collection of all McKay graphs for a given group G encodes, in a sense, its character table. Such graphs were also used by McKay to provide a bijection between the finite subgroups of SU(2) and the affine Dynkin diagrams of types A,D,E , the bijection given by considering the appropriate McKay graphs. In this paper, we classify all (undirected) trees which are McKay graphs of finite groups and describe the corresponding pairs (G,ρ) ; this classification turns out to be very concise. Moreover, we give a partial classification of McKay graphs which are forests, and construct some non-trivial examples of such forests.
Original languageEnglish
StatePublished - 4 Sep 2021


  • Mathematics - Representation Theory
  • Mathematics - Combinatorics


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