The goal of this work is to give a new unified axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras. Building upon fundamental works by Young and Kazhdan-Lusztig (and motivated by ideas of Vershik and Ram), we propose a direct combinatorial construction. For simply laced Coxeter groups, this assumption yields explicit simple representation matrices, generalizing the Young forms. For the symmetric groups the resulting representations are completely classified and contain the irreducible ones. \vskip .1in \noindent This is a joint work with Ron Adin and Francesco Brenti.