Quantum McKay correspondence and global dimensions for fusion and module-categories associated with Lie groups

JOURNAL OF ALGEBRA

卷:398

Article

Coquereaux, R.^1,2 

[1] Inst Nacl Matemat Pura & Aplicada, IMPA, Rio De Janeiro, Brazil

[2] UMI CNRS IMPA 2924, Paris, France

关键词: Lie groups;    Fusion categories;    Conformal field theories;    Quantum symmetries;   

DOI  :  10.1016/j.jalgebra.2013.09.030

来源: Elsevier

【 摘 要 】

Global dimensions for fusion categories A(k)(G) defined by a pair (G,k), where G is a Lie group and k a positive integer, are expressed in terms of Lie quantum superfactorial functions. The global dimension is defined as the square sum of quantum dimensions of simple objects, for the category of integrable modules over an affine Lie algebra at some level. The same quantities can also be defined from the theory of quantum groups at roots of unity or from conformal field theory WZW models. Similar results are also presented for those associated module-categories that can be obtained via conformal embeddings (they are quantum subgroups of a particular kind). As a side result, we express the classical (or quantum) Weyl denominator of simple Lie groups in terms of classical (or quantum) factorials calculated for the exponents of the group. Some calculations use the correspondence existing between periodic quivers for simply-laced Lie groups and fusion rules for module-categories associated with A(k)(SU(2)). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free