  Hecke algebras are beautiful q-extensions of Coxeter groups. In this paper,
we prove several results on their characters, with an emphasis on characters
induced from trivial and sign representations of parabolic subalgebras. While
most of the results in type A are known, our proofs are of a combinatorial
nature, and generalize to (partial) results in types B and C. We also present
complete descriptions of such characters for type I.

Combinatorics;Representation Theory