The Oscillator Character Formula, for Isometry Groups of Split Forms in Deep Stable Range

Andrzej Daszkiewicz and Tomasz Przebinda Department of Mathematics, N. Copernicus University, 87-100 Toruń, Poland Department of Mathematics, University of Oklahoma, Norman, OK, 73019, USA Abstract. Let e G and e G′ be a reductive dual pair of the type mentioned in the title, with e G the smaller member. Let Π and Π′ be unitary representations of e G, e G′ which occur in Howe’s correspondence. We express the distribution character of Π′ in terms of the character of Π via an explicit integral kernel operator.