  In 2014, Braverman, Kazhdan, Patnaik and Bardy-Panse, Gaussent and Rousseau
associated Iwahori-Hecke algebras to Kac-Moody groups over non-Archimedean
local fields. In a previous paper, we defined and studied their principal
series representations. In 1982, Kato provided an irreducibility criterion for
these representations, in the reductive case. We had obtained partially this
criterion in the Kac-Moody case. In this paper, we prove this criterion in the
Kac-Moody case.
