Local theta correspondence between supercuspidal representations, Ann. Sci. Éc. Norm. Supér, 2018
Corollary 5.11, \Gamma+\mathfrak g_{x,r^+} should be \Gamma+\mathfrak g_{x,-r^+}. The proof was correct.
Invariants and K-spectrums of local theta lifts
The condition (\dagger) (on page 180) should also include the case when (G,G') = (\mathrm{Sp}_{2n}(\mathbb C), \mathrm{O}_{4n}(\mathbb C)) and \rho is the trivial representation. In fact, in this case \Theta(\rho) has two irreducible constituents (See “Lee Soo Teck, Zhu Chenbo, Degenerate principal series and local theta correspondence III”).
Generic Hecke algebra and theta correspondence over finite fields
In Theorem 1.1 (eq. (1.8) on page 5; restated in Section 5.4 on page 35), c(\pi) should be 2c(\pi): the conservation relation should read n_{\mathcal{V}'_V}(\pi) + n_{\widetilde{\mathcal{V}}'_V}(\pi) + 2c(\pi) = 2\dim V + \delta, which is exactly what the proof in Section 5.4 yields.