Chern-Simons matrix models and Stieltjes-Wigert polynomials
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...
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Veröffentlicht in: | Journal of mathematical physics 2007-02, Vol.48 (2), p.023507-023507-20 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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-Szegö 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. |
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ISSN: | 0022-2488 1089-7658 |
DOI: | 10.1063/1.2436734 |