On First Occurrence in the Local Theta Correspondence

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Formal degrees and local theta correspondence (2013, background): “Harris-Kudla-Sweet [28] and Kudla-Rallis [47] discovered that the first occurrence indices of π for two closely related Witt towers {Vr} and {V ′ r } are not independent of each other.”
Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups (2009, methodology): “1 in the reference [KR], so let us explain how it follows from the results there (plus a little extra work).”
Conservation relations for local theta correspondence (2012, methodology): “(b) For orthogonal-symplectic dual pairs and π supercuspidal, the conservation relations were due to Kudla and Rallis [KR3].”
On the Howe duality conjecture in classical theta correspondence (2014, methodology): “It amounts to an attempt to prove the Howe duality conjecture using the techniques and principles found in [4] and [5], supplemented by [6], so as to remove the p 6= 2 assumption in Waldspurger’s theorem.”