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Homological properties of quantised Borel-Schur algebras and resolutions of quantised Weyl modules. (English) Zbl 1348.20049

Summary: We continue the development of the homological theory of quantum general linear groups previously considered by the first author. The development is used to transfer information to the representation theory of quantised Schur algebras. The acyclicity of induction from some rank-one modules for quantised Borel-Schur subalgebras is deduced. This is used to prove the exactness of the complexes recently constructed by Boltje and Maisch, giving resolutions of the co-Specht modules for Hecke algebras.

MSC:

20G05 Representation theory for linear algebraic groups
20G43 Schur and \(q\)-Schur algebras
20C30 Representations of finite symmetric groups
20C08 Hecke algebras and their representations
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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References:

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