The Garnir relations for Weyl groups of type \(C_n\). (Q1010794)
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scientific article; zbMATH DE number 5540978
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Garnir relations for Weyl groups of type \(C_n\). |
scientific article; zbMATH DE number 5540978 |
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The Garnir relations for Weyl groups of type \(C_n\). (English)
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7 April 2009
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Summary: The Garnir relations play a very important role in giving combinatorial constructions of representations of the symmetric groups. For the Weyl groups of type \(C_n\), having obtained the alternacy relation, we give an explicit combinatorial description of the Garnir relation associated with a \(\Delta\)-tableau in terms of root systems. We then use these relations to find a \(K\)-basis for the Specht modules of the Weyl groups of type \(C_n\).
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Garnir relations
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representations of symmetric groups
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Weyl groups
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tableaux
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root systems
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Specht modules
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