Iwahori-Hecke Algebras and their Representation Theory - Cherednik, Ivan a Markov, Yavor a Howe, Roger E. a Lusztig, George

Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type.