WKB-expansion of the HarishChandra-Itzykson-Zuber integral for arbitrary beta

Details WKB-expansion of the HarishChandra-Itzykson-Zuber integral for arbitrary beta WKB-expansion of the HarishChandra-Itzykson-Zuber integral for arbitrary beta

2006-04-18

arxiv.org/abs/math-ph/0604041v1

Physics

Mathematical Physics

72 pages

Scientific paper

10.1143/PTP.116.441

This article is devoted to the asymptotic expansion of the generalized Harish Chandra-Itzykson-Zuber matrix integral for non-unitary symmetries characterized by a parameter beta(as usual beta =1,2 and 4 correspond to the orthogonal, unitary and symplectic group integrals). A WKB-expansion for f is derived from the heat kernel differential equation, for general values of k and beta. From an expansion in terms of zonal polynomials, one obtain an expansion in powers of the tau's for beta=1, and generalizations are considered for general beta. A duality relation, and a transformation of products of pairs of symmetric functions into tau polynomials, is used to obtain the expression for f(tau ij) for general beta.

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