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Overgroups of Irreducible Linear Groups, I

✍ Scribed by Ben Ford

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
475 KB
Volume
181
Category
Article
ISSN
0021-8693

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✦ Synopsis

The natural module for Y will be denoted by W. If W is irreducible as an X-module, then ␦ will denote its T -high weight. We will always X Ž .

Ε½ . Ε½ . assume that Y is the smallest of SL W , SO W , Sp W containing X. To justify this assumption, we must eliminate the situation when X -Y -Ε½ . Ε½ . Ε½ . SL W , Y s SO W , or Sp W , and V is a reducible Y-module, but an irreducible G-module. Assume we have such a situation.

² : If X s D and s g G, then X s -Y because Y has no outer auto-4 ˜2 : morphisms of order 3. In this case let X s X s ; otherwise set X s X.

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