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

Two-parameter quantum vertex representations via finite groups and the McKay correspondence

We introduce two-parameter quantum toroidal algebras of simply laced types and provide their group theoretic realization using finite subgroups of $SL_2(\mathbb C)$ via McKay correspondence. In particular our construction contains a realization of the vertex representation of the two-parameter quantum affine algebras of $ADE$ types.

Quantum vertex representations via finite groups and the McKay correspondence

We establish a $q$-analog of our recent work on vertex representations and the McKay correspondence. For each finite group $Γ$ we construct a Fock space and associated vertex operators in terms of wreath products of $Γ\times \mathbb C^{\times}$ and the symmetric groups. An important special case is obtained when $Γ$ is a finite subgroup of $SU_2$, where our construction yields a group theoretic realization of the representations of the quantum affine and quantum toroidal algebras of $ADE$ type.

Generalized Twisted Quantum Doubles and the McKay Correspondence

We consider a class of quasi-Hopf algebras which we call \emph{generalized twisted quantum doubles}. They are abelian extensions $H = \mb{C}[\bar{G}] \bowtie \mb{C}[G]$ ($G$ is a finite group and $\bar{G}$ a homomorphic image), possibly twisted by a 3-cocycle, and are a natural generalization of the twisted quantum double construction of Dijkgraaf, Pasquier and Roche. We show that if $G$ is a subgroup of $SU_2(\mb{C})$ then $H$ exhibits an orbifold McKay Correspondence: certain fusion rules of $H$ define a graph with connected components indexed by conjugacy classes of $\bar{G}$, each connecte…

McKay Correspondence for semisimple Hopf actions on regular graded algebras, I

In establishing a more general version of the McKay correspondence, we prove Auslander's theorem for actions of semisimple Hopf algebras H on noncommutative Artin-Schelter regular algebras A of global dimension two, where A is a graded H-module algebra, and the Hopf action on A is inner faithful with trivial homological determinant. We also show that each fixed ring A^H under such an action arises an analogue of a coordinate ring of a Kleinian singularity.

通过有限群和McKay对应的顶点表示

Vertex representations via finite groups and the McKay correspondence

本文基于有限群及虚特征标，利用圈积表示环构造Fock空间与顶点算子，还原特征标表，并在 $Γ$ 为 $SU_2$ 有限子群时给出 $ADE$ 型仿射与环面李代数基本表示的群论实现，提出McKay对应的新形式。

通过自旋群和 McKay 对应构造的扭顶点表示

Twisted vertex representations via spin groups and the McKay correspondence

本文利用有限群虚特征标与自旋圈积群的超自旋特征标构造扭顶点算子，实现扭仿射和扭环形代数基本表示，并导出自旋特征标表。