# Pizzetti Formulae for Stiefel Manifolds and Applications

Coulembier K, Kieburg M (2015)
Letters in Mathematical Physics 105(10): 1333-1376.

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Journal Article | Published | English

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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 . 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.
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Coulembier K, Kieburg M. Pizzetti Formulae for Stiefel Manifolds and Applications. Letters in Mathematical Physics. 2015;105(10):1333-1376.
Coulembier, K., & Kieburg, M. (2015). Pizzetti Formulae for Stiefel Manifolds and Applications. Letters in Mathematical Physics, 105(10), 1333-1376. doi:10.1007/s11005-015-0774-x
Coulembier, K., and Kieburg, M. (2015). Pizzetti Formulae for Stiefel Manifolds and Applications. Letters in Mathematical Physics 105, 1333-1376.
Coulembier, K., & Kieburg, M., 2015. Pizzetti Formulae for Stiefel Manifolds and Applications. Letters in Mathematical Physics, 105(10), p 1333-1376.
K. Coulembier and M. Kieburg, “Pizzetti Formulae for Stiefel Manifolds and Applications”, Letters in Mathematical Physics, vol. 105, 2015, pp. 1333-1376.
Coulembier, K., Kieburg, M.: Pizzetti Formulae for Stiefel Manifolds and Applications. Letters in Mathematical Physics. 105, 1333-1376 (2015).
Coulembier, Kevin, and Kieburg, Mario. “Pizzetti Formulae for Stiefel Manifolds and Applications”. Letters in Mathematical Physics 105.10 (2015): 1333-1376.
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