Corrigendum to “Geometric conditions for □-irreducibility of certain representations of the general linear group over a non-archimedean local field” [Adv. Math. 339 (2018) 113–190], (S0001870818303657), (10.1016/j.aim.2018.09.027)

The main results of [1] are correct. However, there is an error in the statement and proof of [1, Corollary 9.6]. As a result, there is an additional basic case which needs to be considered by the same techniques as in [1, §8]. More precisely, the formula for [Formula presented] on the fourth line of [1, p. 179] (the case [Formula presented]) is incorrect. The correct formula is [Formula presented] This means that in [1, Corollary 9.6] we also have to allow the case [Formula presented]r, i.e., the family [Formula presented] Correspondingly, we need to consider this family in the analysis of the basic cases in [1, §8]. This is very similar to the other cases considered there. First, as in [1, Remark 6.12], [Formula presented] does not satisfy the condition (GLS) of [1, §4]. Moreover, if [Formula presented], then in the language of [1, §8], the pair [Formula presented] is a splitting for π with double socle [Formula presented]. This is proved as in [1, Lemma 8.5] except that now [Formula presented]. Finally, replacing [Formula presented] by [Formula presented] we can apply [1, Lemma 8.6] to conclude, as in the proof of [1, Proposition 8.3], that [Formula presented] Thus, π is not □-irreducible. The rest of the argument in [1, §9] stays the same. All other assertions of [1], including the main results, are not affected.