REVIEW 8 cited by
On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
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.
Forward citations
Cited by 8 Pith papers
-
Proliferation Transitions for Non-Abelian Anyons
A SymTFT-based construction realizes proliferation transitions for any condensable algebra in a modular tensor category, with the symmetry fixed by the transparent lines of the algebra's generated subcategory.
-
Hypergroup Symmetry in Relative Quantum Field Theories and Chiral Algebras
Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left...
-
Proliferation transitions from a topological phase in $2+1$ dimensions
A general 2+1d transition theory out of a topological phase, driven by one Abelian anyon, is constructed and shown to depend on a single integer parameter, with p=0 giving gauging.
-
Fusion rules and rigidity for weight modules over the simple admissible affine $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator superalgebras
Rigidity of weight module categories for admissible affine sl(2) and N=2 superconformal minimal models is proved, together with the conjectured fusion product decompositions, including non-semisimple summands.
-
Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
-
ADE triality via (non-)invertible symmetry gauging
Gauging a non-invertible symmetry exchanges the D7 and E6 minimal models, completing the ADE triality.
-
Anyon Condensation in Virasoro TQFT: Wormhole Factorization
Condensing a diagonal anyon in Virasoro TQFT factorizes wormhole partition functions and produces Liouville CFT on the two boundary surfaces.
-
On Hecke and asymptotic categories for a family of complex reflection groups
Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.
Discussion (0). Continue with ORCID to comment.