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Homological properties of quantised Borel–Schur algebras and resolutions of quantised Weyl modules

Authors
  • Donkin, Stephen
  • Santana, Ana Paula
  • Yudin, Ivan1, 2, 3, 1, 4
  • 1 Department of Mathematics
  • 2 University of York
  • 3 CMUC
  • 4 University of Coimbra
Type
Published Article
Journal
Journal of Algebra
Publication Date
Jan 01, 2013
Volume
402
Pages
120–157
Identifiers
DOI: 10.1016/j.jalgebra.2013.10.036
Source
Elsevier
Keywords
License
Unknown

Abstract

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.

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