Hecke Algebras with Unequal Parameters

Hecke algebras arise in representation theory as endomorphism algebras of induced representations. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra. This book extends the theory of the KL-basis to a general class of Hecke algebras.