# Chern-Simons matrix models and Stieltjes-Wigert polynomials

## Abstract

Employing the random matrix formulation of Chern-Simons theory on Seifert manifolds, we show how the Stieltjes-Wigert orthogonal polynomials are useful in exact computations in Chern-Simons matrix models. We construct a biorthogonal extension of the Stieltjes-Wigert polynomials, not available in the literature, necessary to study Chern-Simons matrix models when the geometry is a lens space. We also study the relationship between Stieltjes-Wigert and Rogers-Szegoe polynomials and the corresponding equivalence with a unitary matrix model. Finally, we give a detailed proof of a result that relates quantum dimensions with averages of Schur polynomials in the Stieltjes-Wigert ensemble.

- Authors:

- Laboratoire de Physique Theorique de L'Ecole Normale Superieure, 24 rue L'Homond 75231, Paris Cedex 05 (France)
- (IEEC/CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Parell-2A Planta, E-08193 Bellaterra, Barcelona (Spain)

- Publication Date:

- OSTI Identifier:
- 20929644

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 2; Other Information: DOI: 10.1063/1.2436734; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CALCULATION METHODS; GEOMETRY; MATHEMATICAL SPACE; MATRICES; POLYNOMIALS; RANDOMNESS

### Citation Formats

```
Dolivet, Yacine, Tierz, Miguel, and Institut d'Estudis Espacials de Catalunya.
```*Chern-Simons matrix models and Stieltjes-Wigert polynomials*. United States: N. p., 2007.
Web. doi:10.1063/1.2436734.

```
Dolivet, Yacine, Tierz, Miguel, & Institut d'Estudis Espacials de Catalunya.
```*Chern-Simons matrix models and Stieltjes-Wigert polynomials*. United States. doi:10.1063/1.2436734.

```
Dolivet, Yacine, Tierz, Miguel, and Institut d'Estudis Espacials de Catalunya. Thu .
"Chern-Simons matrix models and Stieltjes-Wigert polynomials". United States.
doi:10.1063/1.2436734.
```

```
@article{osti_20929644,
```

title = {Chern-Simons matrix models and Stieltjes-Wigert polynomials},

author = {Dolivet, Yacine and Tierz, Miguel and Institut d'Estudis Espacials de Catalunya},

abstractNote = {Employing the random matrix formulation of Chern-Simons theory on Seifert manifolds, we show how the Stieltjes-Wigert orthogonal polynomials are useful in exact computations in Chern-Simons matrix models. We construct a biorthogonal extension of the Stieltjes-Wigert polynomials, not available in the literature, necessary to study Chern-Simons matrix models when the geometry is a lens space. We also study the relationship between Stieltjes-Wigert and Rogers-Szegoe polynomials and the corresponding equivalence with a unitary matrix model. Finally, we give a detailed proof of a result that relates quantum dimensions with averages of Schur polynomials in the Stieltjes-Wigert ensemble.},

doi = {10.1063/1.2436734},

journal = {Journal of Mathematical Physics},

number = 2,

volume = 48,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

DOI: 10.1063/1.2436734

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