skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
;  [1];  [2]
  1. Laboratoire de Physique Theorique de L'Ecole Normale Superieure, 24 rue L'Homond 75231, Paris Cedex 05 (France)
  2. (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}
}