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Kazhdan-Lusztig cells and decomposition numbers
Author(s):
Meinolf
Geck
Journal:
Represent. Theory
2
(1998),
264-277.
MSC (1991):
Primary 20C20;
Secondary 20G99
Posted:
June 15, 1998
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Abstract:
We consider a generic Iwahori-Hecke algebra  associated with a finite Weyl group. Any specialization of  gives rise to a corresponding decomposition matrix, and we show that the problem of computing that matrix can be interpreted in terms of Lusztig's map from  to the asymptotic algebra  . This interpretation allows us to prove that the decomposition matrices always have a lower uni-triangular shape; moreover, we determine these matrices explicitly in the so-called defect  case.
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Additional Information:
Meinolf
Geck
Affiliation:
UFR de Mathématiques and UMR 7586 du CNRS, Université Paris 7, 2 Place Jussieu, 75251 Paris, France
Email:
geck@math.jussieu.fr
DOI:
10.1090/S1088-4165-98-00042-9
PII:
S 1088-4165(98)00042-9
Received by editor(s):
December 11, 1997
Received by editor(s) in revised form:
April 27, 1998
Posted:
June 15, 1998
Copyright of article:
Copyright
1998,
American Mathematical Society
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