Yang–Baxter bases of 0-Hecke algebras and representation theory of 0-Ariki–Koike–Shoji algebras

After reformulating the representation theory of 0-Hecke algebras in an appropriate family of Yang–Baxter bases, we investigate certain specializations of the Ariki–Koike algebras, obtained by setting q=0 in a suitably normalized version of Shoji's presentation. We classify the simple and projective modules, and describe restrictions, induction products, Cartan invariants and decomposition matrices. This allows us to identify the Grothendieck rings of the towers of algebras in terms of certain graded Hopf algebras known as the Mantaci–Reutenauer descent algebras, and Poirier quasi-symmetric functions. We also describe the Ext-quivers, and conclude with numerical tables.