Formal degrees and local theta correspondence

By W. Gan, Atsushi Ichino. Inventiones Mathematicae, 2013

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On the Howe duality conjecture in classical theta correspondence (2014, background): “3, the assumption that p 6= 2 can be totally removed from all the results in [2] (on the local Shimura correspondence) and also parts of [1] (those dealing with the almost equal rank case, such as the results on Prasad’s conjecture in [1, Appendix C]).”
The Gross–Prasad conjecture and local theta correspondence (2014, methodology): “The following summarises some results of [10]: Theorem 4.”
Local theta correspondence of tempered representations and Langlands parameters (2016, methodology): “ui´c’s work. For example, the conservation relation is now known and we do exploit it to simplify life. •we make use of a wider spectrum of tools than Mui´c. For example, we use results of Gan–Ichino [GI1] on the behaviour of the standard gamma factors and Plancherel measures in the local theta corr”
The Howe Duality Conjecture (2014, background): “• In joint work [2, 3] of A Ichino and W T Gan, Question (c) was fully addressed for dual pairs of almost equal size, in terms of the local Langlands correspondence.”