Editorial Boar d
Jerry L . Bon a (Chair ) Nicola i Reshetikhi n
Jean-Luc Brylinsk i Leonar d L . Scot t
The autho r gratefull y acknowledge s th e suppor t o f th e
Sonderforschungsbereich 34 3 a t th e Universita t Bielefel d
and o f a U200 0 Fellowshi p a t th e Universit y o f Sydney .
1991 Mathematics Subject Classification. Primar y 20C30 , 16G99;
Secondary 05E10, 20G05 , 20C20 .
ABSTRACT. Thi s boo k give s a full y self-containe d introductio n t o th e modula r representatio n the -
ory o f the Iwahori-Heck e algebra s o f the symmetri c group s an d o f the associate d g-Schu r algebras .
The mai n landmark s tha t w e reac h ar e th e classificatio n o f th e simpl e module s an d th e block s
of thes e algebras . Alon g th e wa y th e theor y o f cellula r algebra s i s develope d an d a n analogu e
of Jantzen' s su m formul a i s proved . Combinatoria l motif s pervad e th e text , wit h standar d an d
semistandard tableau x bein g use d t o inde x explici t (cellular ) bases ; thes e base s ar e particularl y
well adapte d t o th e representatio n theory . Thi s result s i n clea n an d elegan t proof s o f mos t o f th e
basic result s abou t thes e algebras . Th e final chapte r give s a surve y o f som e recen t an d excitin g
developments i n th e field an d discusse s ope n problems .
The boo k shoul d b e accessibl e t o advance d graduat e student s an d als o usefu l t o researcher s i n
the field.
Library o f Congres s Cataloging-in-Publicatio n Dat a
Mat has, Andrew , 1966-
Iwahori-Hecke algebra s an d Schu r algebra s o f th e symmetri c grou p / Andre w Mathas .
p. cm . (Universit y lectur e series , ISS N 1047-3998 ; v. 15)
Includes bibliographica l reference s an d indexes .
ISBN 0-8218-1926-7 (alk . paper )
1. Symmetr y groups . 2 . Representations o f algebras . I . Title . II . Series : Universit y lectur e
series (Providence , R.I. ) ; 15.
QA 174.2.M38 1999
512'.2-dc21 99-29310
CIP
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© 1999 b y th e America n Mathematica l Society . Al l right s reserved .
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