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

dc.creatorKirillov Jr, Alexander
dc.creatorOstrik, Viktor
dc.date2001-01-26
dc.date2001-12-03
dc.date.accessioned2026-07-07T04:39:49Z
dc.date.available2026-07-07T04:39:49Z
dc.descriptionThe goal of this paper is to classify ``finite subgroups in U_q sl(2)'' where $q=e^{\piı/l}$ 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.
dc.description37 pages. New in v3: added more references and details of proofs; rewritten introduction; fixed gap in the proof of uniqueness for type E_8
dc.identifierhttps://arxiv.org/abs/math/0101219
dc.identifierhttp://arxiv.org/abs/math/0101219
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60826
dc.subjectQuantum Algebra
dc.titleOn q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories
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