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Some simple modules for the restricted Cartan-type Lie algebras

✍ Scribed by Randall R. Holmes; Chaowen Zhang

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
287 KB
Volume
173
Category
Article
ISSN
0022-4049

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✦ Synopsis

Every simple module having character height at most one for a restricted Cartan-type Lie algebra g can be realized as a quotient of a module obtained by starting with a simple module S for the homogeneous component of degree zero in the natural grading of g, extending the action trivially to positive components and inducing up to g. It is shown that if S is not restricted, or if it is restricted and its maximal vector does not have exceptional weight, then the induced module is already simple.

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