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Pré-Publication, Document De Travail Année : 2006

Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

Résumé

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials prod tr{X^{p_1} Omega Y^{q_1} Omega^dagger X^{p_2} ... with the weight exp tr{X Omega Y Omega^dagger} are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat-Heckman's theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.

Dates et versions

hal-00108986 , version 1 (23-10-2006)

Identifiants

Citer

A. Prats Ferrer, B. Eynard, P. Di Francesco, J. -B. Zuber. Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups. 2006. ⟨hal-00108986⟩
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