TITLE: Irreducible Representations of Finite Coxeter Groups
QUESTION [7 upvotes]: The Coxeter group is defined as
$$S = \langle s_i : s_i^2 = (s_i s_j)^{m_{ij}} = 1 \rangle $$
Does it have an irreducible representation of dimension >2 for $S$ finite? 
Is there a reference on this subject i.e. to find irreps of finite $S$?
For the lowest two cases: $$ i=1;   S=C_2$$ $$ i=1,2; S=Dih(2m)$$ so that there is no irrep of dim >2 .  
Thanks.

REPLY [2 votes]: The standard reference for such matters is Jim Humphrey's "Reflection Groups and Coxeter Groups". This link might also be of interest.