Universität zu Köln

Coulembier, Kevin ORCID: 0000-0003-0996-3965 and Kieburg, Mario (2015). Pizzetti Formulae for Stiefel Manifolds and Applications. Lett. Math. Phys., 105 (10). S. 1333 - 1377. DORDRECHT: SPRINGER. ISSN 1573-0530

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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 . 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Coulembier, Kevin UNSPECIFIED orcid.org/0000-0003-0996-3965 UNSPECIFIED Kieburg, Mario UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-392456
DOI:	10.1007/s11005-015-0774-x
Journal or Publication Title:	Lett. Math. Phys.
Volume:	105
Number:	10
Page Range:	S. 1333 - 1377
Date:	2015
Publisher:	SPRINGER
Place of Publication:	DORDRECHT
ISSN:	1573-0530
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language RANDOM-MATRIX THEORY; DIRAC OPERATOR; RECURSIVE CONSTRUCTION; RADIAL FUNCTIONS; INTEGRALS; SYMMETRY; SPECTRUM; UNITARY Multiple languages Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/39245