On bases for infinite little/infinitesimal \(q\)-Schur algebras (Q1040664)
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scientific article; zbMATH DE number 5638431
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On bases for infinite little/infinitesimal \(q\)-Schur algebras |
scientific article; zbMATH DE number 5638431 |
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On bases for infinite little/infinitesimal \(q\)-Schur algebras (English)
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25 November 2009
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Let \(k\) be a field containing a primitive root of unity of order at least 3. The author introduces the infinite little \(q\)-Schur algebra \(u_k(\infty, r)\) over \(k\) as an (infinite-dimensional) subalgebra of the infinite \(q\)-Schur algebra \(S_k(\infty, r)\). Several bases of monomial, Beilinson-Lusztig-MacPherson and PBW type for \(u_k(\infty, r)\) are exhibited. Constructions of bases of monomial and PBW type for the infinite version of the infinitesimal \(q\)-Schur algebra are given.
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\(q\)-Schur algebras
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infinite little and infinitesimal \(q\)-Schur algebras
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monomial
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BLM and PBW bases
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