Mathematics – Quantum Algebra
Scientific paper
2001-01-26
Mathematics
Quantum Algebra
37 pages. New in v3: added more references and details of proofs; rewritten introduction; fixed gap in the proof of uniqueness
Scientific paper
The goal of this paper is to classify ``finite subgroups in U_q sl(2)'' where $q=e^{\pi\i/l}$ 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.
Alexander Kirillov Jr.
Ostrik Viktor
No associations
LandOfFree
On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-390065