On complexes relating the Jacobi-Trudy identity with the Bernstein- Gelfand-Gelfand resolution (Q1118033)
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scientific article; zbMATH DE number 4093754
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On complexes relating the Jacobi-Trudy identity with the Bernstein- Gelfand-Gelfand resolution |
scientific article; zbMATH DE number 4093754 |
Statements
On complexes relating the Jacobi-Trudy identity with the Bernstein- Gelfand-Gelfand resolution (English)
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1988
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Let K be the Grothendieck group of polynomial representations of GL(n,C), V(\(\lambda)\) be the class of the irreducible representation with the highest weight \(\lambda\). The Jacobi-Trudy identity gives an expression for V(\(\lambda)\) in K in terms of symmetric powers \(S_ r(V)\) of the standard representation \(V=C^ n\) of GL(n,C). The author shows the relation of the Jacobi-Trudy identity to the resolution of V(\(\lambda)\) by Verma modules (the Bernstein-Gelfand-Gelfand resolution).
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Grothendieck group
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polynomial representations
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highest weight
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Jacobi- Trudy identity
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symmetric powers
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Verma modules
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Bernstein-Gelfand- Gelfand resolution
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