Coincidence of algebraic and smooth theta correspondences

Bao, YiXin; Sun, BinYong

doi:10.1090/ert/508

Coincidence of algebraic and smooth theta correspondences
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by YiXin Bao and BinYong Sun

Represent. Theory 21 (2017), 458-466

DOI: https://doi.org/10.1090/ert/508

Published electronically: November 1, 2017

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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 $\mathbb R$ agree 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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