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A Cauchy Harish-Chandra integral, for a real reductive dual pair. (English) Zbl 0953.22014
For a real irreducible dual pair $$G$$, $$G'$$ in a metaplectic group, with $$\text{rank }G\leq \text{rank }G'$$, the author constructs an integral kernel operator from the space of invariant eigendistributions on $$G$$ to the space of invariant distributions on $$G'$$, and conjectures that this operator is compatible with Howe’s correspondence on the level of characters. The construction indicates a direct link between the Cauchy determinant identity and the Howe correspondence.

MSC:
 2.2e+46 Representations of Lie and linear algebraic groups over real fields: analytic methods
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