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Medientyp:
E-Artikel
Titel:
On the Decomposition Numbers of the Finite General Linear Groups
Beteiligte:
Dipper, Richard
Erschienen:
American Mathematical Society, 1985
Erschienen in:
Transactions of the American Mathematical Society, 290 (1985) 1, Seite 315-344
Sprache:
Englisch
ISSN:
0002-9947
Entstehung:
Anmerkungen:
Beschreibung:
Let G = GLn(q), q a prime power, and let r be an odd prime not dividing q. Let s be a semisimple element of G of order prime to r and assume that r divides q°(Λ)- 1 for all elementary divisors Λ of s. Relating representations of certain Hecke algebras over symmetric groups with those of G, we derive a full classification of all modular irreducible modules in the r-block Bsof G with semisimple part s. The decomposition matrix D of Bsmay be partly described in terms of the decomposition matrices of the symmetric groups corresponding to the Hecke algebras above. Moreover D is lower unitriangular. This applies in particular to all r-blocks of G if r divides q - 1. Thus, in this case, the r-decomposition matrix of G is lower unitriangular.