# Orders and dimensions for sl(2) or sl(3) module categories and boundary conformal field theories on a torus

## Abstract

After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and cosemisimple blocks of the corresponding weak bialgebras (quantum groupoids), tables of quantum dimensions and orders, and tables describing induction-restriction. For reasons of size, the sl(3) tables of induction are only given for theories with self-fusion (existence of a monoidal structure)

- Authors:

- Centre de Physique Theorique, UMR 6207 du CNRS et des Universites Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var, affilie a la FRUMAM (FR 2291), Luminy Case 907, F-13288 Marseille Cedex 9 (France)
- (CBPF), Rua Dr. Xavier Sigaud, 150 Rio de Janeiro (Brazil)

- Publication Date:

- OSTI Identifier:
- 20929689

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2714000; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; CONFORMAL INVARIANCE; QUANTUM FIELD THEORY; SL GROUPS

### Citation Formats

```
Coquereaux, R., Schieber, G., and Centro Brasileiro de Pesquisas Fisicas.
```*Orders and dimensions for sl(2) or sl(3) module categories and boundary conformal field theories on a torus*. United States: N. p., 2007.
Web. doi:10.1063/1.2714000.

```
Coquereaux, R., Schieber, G., & Centro Brasileiro de Pesquisas Fisicas.
```*Orders and dimensions for sl(2) or sl(3) module categories and boundary conformal field theories on a torus*. United States. doi:10.1063/1.2714000.

```
Coquereaux, R., Schieber, G., and Centro Brasileiro de Pesquisas Fisicas. Sun .
"Orders and dimensions for sl(2) or sl(3) module categories and boundary conformal field theories on a torus". United States.
doi:10.1063/1.2714000.
```

```
@article{osti_20929689,
```

title = {Orders and dimensions for sl(2) or sl(3) module categories and boundary conformal field theories on a torus},

author = {Coquereaux, R. and Schieber, G. and Centro Brasileiro de Pesquisas Fisicas},

abstractNote = {After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and cosemisimple blocks of the corresponding weak bialgebras (quantum groupoids), tables of quantum dimensions and orders, and tables describing induction-restriction. For reasons of size, the sl(3) tables of induction are only given for theories with self-fusion (existence of a monoidal structure)},

doi = {10.1063/1.2714000},

journal = {Journal of Mathematical Physics},

number = 4,

volume = 48,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2714000

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