The Oscillator Character Formula, for isometry groups of split forms in deep stable range

Let  G and  G' be a reductive dual pair of the type mentioned in the title, with G the smaller member. Let P and P' be unitary representations of  (the double covers of) G,  G' which occur in Howe's Correspondence. We express the distribution character of P' in terms of the character of P via an explicit integral kernel operator.

Appeared in Invent. Math. 123, 349--376 (1996)