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Jucys–Murphy Elements and Weingarten Matrices

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Abstract

We provide a compact proof of the recent formula of Collins and Matsumoto for the Weingarten matrix of the orthogonal group using Jucys–Murphy elements.

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References

  1. Banica, T.: The orthogonal Weingarten formula in compact form. Lett. Math. Phys. 91 (2010). arXiv:0906.4694; doi:10.1007/s11005-009-0363-y

  2. Collins B.: Moments and cumulants of polynomial random variables on unitary groups, the Itzykson–Zuber integral, and free probability. Int. Math. Res. Not. 17, 953–982 (2003) arXiv:math-ph/0205010

    Article  Google Scholar 

  3. Collins, B., Matsumoto, S.: On some properties of orthogonal Weingarten functions. (Preprint, 2009). arXiv:0903.5143

  4. Collins B., Śniady P.: Integration with respect to the Haar measure on unitary, orthogonal and symplectic group. Comm. Math. Phys. 264(3), 773–795 (2006) arXiv: math-ph/0402073

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. Jucys A.-A.: Symmetric polynomials and the center of the symmetric group ring. Rep. Mathematical Phys. 5(1), 107–112 (1974)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Matsumoto, S., Novak, J.: Symmetric polynomials in Jucys–Murphy elements and the Weingarten function. (Preprint, 2009). arXiv:0905.1992

  7. Murphy G.: A new construction of Young’s seminormal representation of the symmetric groups. J. Algebra 69(2), 287–297 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  8. Novak, J.: Complete homogeneous symmetric polynomials in Jucys–Murphy elements and the Weingarten function. (Preprint, 2009). arXiv:0811.3595

  9. Weingarten D.: Asymptotic behavior of group integrals in the limit of infinite rank. J. Math. Phys. 19(5), 999–1001 (1978)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. Zuber, J.-B.: The large N limit of matrix integrals over the orthogonal group. J. Phys. A 41, 382001 (2008). arXiv:0805.0315; doi:10.1088/1751-8113/41/38/382001

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Authors and Affiliations

  1. UPMC Univ Paris 6, CNRS UMR 7589, LPTHE, 75252, Paris Cedex, France

    Paul Zinn-Justin

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  1. Paul Zinn-Justin
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Correspondence to Paul Zinn-Justin.

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P. Zinn-Justin was supported by EU Marie Curie Research Training Network “ENRAGE” MRTN-CT-2004-005616, ESF program “MISGAM” and ANR program “GRANMA” BLAN08-1-13695.

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Zinn-Justin, P. Jucys–Murphy Elements and Weingarten Matrices. Lett Math Phys 91, 119–127 (2010). https://doi.org/10.1007/s11005-009-0365-9

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  • DOI: https://doi.org/10.1007/s11005-009-0365-9

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