Pizzetti Formulae for Stiefel Manifolds and Applications

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

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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.
Erscheinungsjahr
Zeitschriftentitel
Letters in Mathematical Physics
Band
105
Zeitschriftennummer
10
Seite
1333-1376
ISSN
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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.