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Pizzetti formulae for Stiefel manifolds and applications

(2015) LETTERS IN MATHEMATICAL PHYSICS. 105(10). p.1333-1376
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Abstract
Pizzetti’s formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion Stiefel manifolds in a unifying way. In particular, we propose a new way to calculate group integrals and try to uncover some algebraic structures which manifest themselves for some well-known cases like the Harish-Chandra integral. We apply a particular case of our formula to an Itzykson–Zuber integral for the coset SO(4)/[SO(2)×SO(2)]. This integral naturally appears in the calculation of the two-point correlation function in the transition of the statistics of the Poisson ensemble and the Gaussian orthogonal ensemble in random matrix theory.
Keywords
RECURSIVE CONSTRUCTION, RADIAL FUNCTIONS, QCD, INTEGRALS, ENSEMBLES, SYMMETRY, SPECTRUM, UNITARY, Pizzetti formula, Haar measure, Itzykson-Zuber integral, Howe dual pair, random matrix theory, DIRAC OPERATOR, RANDOM-MATRIX THEORY

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MLA
Coulembier, Kevin, and Mario Kieburg. “Pizzetti Formulae for Stiefel Manifolds and Applications.” LETTERS IN MATHEMATICAL PHYSICS, vol. 105, no. 10, SPRINGER, 2015, pp. 1333–76, doi:10.1007/s11005-015-0774-x.
APA
Coulembier, K., & Kieburg, M. (2015). Pizzetti formulae for Stiefel manifolds and applications. LETTERS IN MATHEMATICAL PHYSICS, 105(10), 1333–1376. https://doi.org/10.1007/s11005-015-0774-x
Chicago author-date
Coulembier, Kevin, and Mario Kieburg. 2015. “Pizzetti Formulae for Stiefel Manifolds and Applications.” LETTERS IN MATHEMATICAL PHYSICS 105 (10): 1333–76. https://doi.org/10.1007/s11005-015-0774-x.
Chicago author-date (all authors)
Coulembier, Kevin, and Mario Kieburg. 2015. “Pizzetti Formulae for Stiefel Manifolds and Applications.” LETTERS IN MATHEMATICAL PHYSICS 105 (10): 1333–1376. doi:10.1007/s11005-015-0774-x.
Vancouver
1.
Coulembier K, Kieburg M. Pizzetti formulae for Stiefel manifolds and applications. LETTERS IN MATHEMATICAL PHYSICS. 2015;105(10):1333–76.
IEEE
[1]
K. Coulembier and M. Kieburg, “Pizzetti formulae for Stiefel manifolds and applications,” LETTERS IN MATHEMATICAL PHYSICS, vol. 105, no. 10, pp. 1333–1376, 2015.
@article{7055822,
  abstract     = {{Pizzetti’s formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion Stiefel manifolds in a unifying way. In particular, we propose a new way to calculate group integrals and try to uncover some algebraic structures which manifest themselves for some well-known cases like the Harish-Chandra integral. We apply a particular case of our formula to an Itzykson–Zuber integral for the coset SO(4)/[SO(2)×SO(2)]. This integral naturally appears in the calculation of the two-point correlation function in the transition of the statistics of the Poisson ensemble and the Gaussian orthogonal ensemble in random matrix theory.}},
  author       = {{Coulembier, Kevin and Kieburg, Mario}},
  issn         = {{1573-0530}},
  journal      = {{LETTERS IN MATHEMATICAL PHYSICS}},
  keywords     = {{RECURSIVE CONSTRUCTION,RADIAL FUNCTIONS,QCD,INTEGRALS,ENSEMBLES,SYMMETRY,SPECTRUM,UNITARY,Pizzetti formula,Haar measure,Itzykson-Zuber integral,Howe dual pair,random matrix theory,DIRAC OPERATOR,RANDOM-MATRIX THEORY}},
  language     = {{eng}},
  number       = {{10}},
  pages        = {{1333--1376}},
  publisher    = {{SPRINGER}},
  title        = {{Pizzetti formulae for Stiefel manifolds and applications}},
  url          = {{http://doi.org/10.1007/s11005-015-0774-x}},
  volume       = {{105}},
  year         = {{2015}},
}

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