On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories

arXivmath/0101219MaRDI QIDQ6470898

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Publication date: 26 January 2001

Abstract: The goal of this paper is to classify ``finite subgroups in U_q sl(2) where $q=e^{pii/l}$ is a root of unity. We propose a definition of such a subgroup in terms of the category of representations of U_q sl(2); we show that this definition is a natural generalization of the notion of a subgroup in a reductive group, and that it is also related with extensions of the chiral (vertex operator) algebra corresponding to sl^(2) at level k=l-2. We show that ``finite subgroups in U_q sl(2) are classified by Dynkin diagrams of types A_n, D_{2n}, E_6, E_8 with Coxeter number equal to $l$, give a description of this correspondence similar to the classical McKay correspondence, and discuss relation with modular invariants in (sl(2))_k conformal field theory.

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