Canonical bases and the conjugating representation of a semisimple group. (Q1858309)
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scientific article; zbMATH DE number 1868172
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Canonical bases and the conjugating representation of a semisimple group. |
scientific article; zbMATH DE number 1868172 |
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Canonical bases and the conjugating representation of a semisimple group. (English)
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13 February 2003
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Let \(G\) be a semisimple simply connected affine algebraic group over an algebraically closed field \(k\) of characteristic zero, \(A(G)\) the \(k\)-algebra of regular functions on \(G\), and \(C(G)\) the subalgebra consisting of class functions (invariant under inner automorphisms). Richardson proved that \(A(G)\) is a free \(C(G)\)-module. A constructive proof is given using Lusztig's work on canonical bases.
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representations
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reductive algebraic groups
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Richardson theorem
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global separation of variables
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canonical bases
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free modules
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