REFERENCES x v
Finally, i t shoul d b e sai d tha t th e accoun t i n Chapte r I I o f these note s reflect s th e
state o f knowledg e a t th e tim e (Marc h 1993) th e lecture s wer e delivered . A t tha t
time, fo r example , th e nor m formul a referre d t o abov e wa s stil l conjectural . I n
Chapter II I I hav e attempte d t o remed y thi s defec t t o som e extent , b y surveyin g
some o f th e mor e recen t development s involvin g th e afHn e Heck e algebra , suc h
as th e nonsymmetri c orthogona l polynomial s E\ (Chapte r III , §6) , a proo f o f th e
norm formul a (an d henc e in particular o f (9 ) above) i n §7 , and Cherednik' s Fourie r
transform (§9) . However , a s th e subjec t i s stil l evolvin g rapidly , thi s surve y i s
necessarily incomplete .
References
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[HO] G . Heckma n an d E . Opdam, Root systems and hyper geometric functions. I—IV , Comp. Math .
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[M] I . G . Macdonald , Some conjectures for root systems, SIA M J . Math . Anal . 13 (1982), 988 -
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[W] K . Wilson , Proof of a conjecture by Dyson, J . Math . Phys . 3 (1962), 1040-1043.
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