We explicitly determine the theta correspondences for $\GSp_4$ and orthogonal similitude groups associated to various quadratic spaces of rank $4$ and $6$. The results are needed in our proof of the local Langlands correspondence for $\GSp_4$.
Deligne--Lusztig constructions for division algebras and the local Langlands correspondence, II
Genericity and contragredience in the local Langlands correspondence
Rectifiers and the local Langlands correspondence: the unramified case
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