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The Cauchy Harish-Chandra integral, for the pair \({\mathfrak u}_{p,q},{\mathfrak u}_1\). (English) Zbl 1204.22008

Summary: For the dual pair considered, the Cauchy Harish-Chandra integral, as a distribution on the Lie algebra, is the limit of the holomorphic extension of the reciprocal of the determinant. We compute that limit explicitly in terms of the Harish-Chandra orbital integrals.

MSC:

22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
22E46 Semisimple Lie groups and their representations
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