Pizzetti formulae for Stiefel manifolds and applications
- Author
- Kevin Coulembier (UGent) and Mario Kieburg
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-7055822
- 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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