Some applications of theta correspondence to branching laws

In this paper, we will use the local theta correspondences for the dual pair $(\mathrm{Sp}(W), \mathrm{O} (V))$ to investigate some branching law problems.

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This research was done when the author was a Visiting Fellow at Tata Institute of Fundamental Research, Mumbai and it was partially supported by the ERC StG grant number 637912 during revision.

Received 21 July 2018

Accepted 22 April 2019

Published 8 April 2020