A character formula for a family of simple modular representations of
$ GL_n $ |
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Authors: | O Mathieu G Papadopoulo |
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Institution: | Université Louis Pasteur, IRMA, 7 rue René Descartes, F-67000 Strasbourg, France, FR Mathematisches Institut, Universit?t Basel, Rheinsprung 21, CH-4051 Basel, Switzerland, CH
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Abstract: | Let K be an algebraically closed field of finite characteristic p, and let be an integer. In the paper, we give a character formula for all simple rational representations of with highest weight any multiple of any fundamental weight. Our formula is slightly more general: say that a dominant weight
λ is special if there are integers such that and . Indeed, we compute the character of any simple module whose highest weight λ can be written as with all are special. By stabilization, we get a character formula for a family of irreducible rational -modules.
Received: June 30, 1997. |
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Keywords: | , Tilting modules, modular representations, character formula, polynomial functors, Verlinde's formula, |
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