Galois irreducibility implies cohomology freeness for KHT Shimura varieties

Given a KHT Shimura variety provided with an action of its unramified Hecke algebra $mathbb T$, we proved in a previous work, see also the work of Caraiani-Scholze for other PEL Shimura varieties, that its localized cohomology groups at a generic maximal ideal $mathfrak m$ of $mathbb T$, appear to be free. In this work, we obtain the same result for $mathfrak m$ such that its associated galoisian $overline{mathbb F}_l$-representation $overline{rho_{mathfrak m}}$ is irreducible.