Coincidence of algebraic and smooth theta correspondences (1611.06298v1)

Published 19 Nov 2016 in math.RT

Abstract: An "automatic continuity" question has naturally occurred since Roger Howe established the local theta correspondence over $\mathbb R$: does the algebraic version of local theta correspondence over $\mathbb R$ agrees with the smooth version? We show that the answer is yes, at least when the concerning dual pair has no quaternionic type I irreducible factor.

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