The first tw o chapters o f these notes reproduce, wit h additiona l detai l here an d
there, the conten t o f the ora l lectures delivered i n March 1993. Fo r example, I have
included th e origina l proo f o f the existenc e theore m (Chapte r II , §§ 6 and 7 ) whic h
previously wa s availabl e onl y i n preprin t form .
The postscrip t (Chapte r III ) perhap s require s a wor d o f explanation . Durin g
the perio d tha t ha s elapse d sinc e thes e lecture s wer e given , th e subjec t ha s en -
joyed considerabl e advanc e an d clarification , mainl y thank s t o th e wor k o f Iva n
Cherednik, wh o perceive d tha t th e affin e Heck e algebra s provide d a ke y t o unloc k
its mysteries . Chapte r II I provide s a brie f surve y o f these recen t developments .
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