Green, R. M. (1999) *The affine q-Schur algebra.* Journal of Algebra, 215 (2). pp. 379-411. ISSN 0021-8693

## Abstract

We introduce an analogue of theq-Schur algebra associated to Coxeter systems of typeÁn − 1. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an affine Hecke algebra of typeÁr − 1, wheren ≥ r. This generalizes the originalq-Schur algebra as defined by Dipper and James, and the new algebra contains the ordinaryq-Schur algebra and the affine Hecke algebra as subalgebras. Using this approach we can prove a double centralizer property. The second construction realizes the affineq-Schur algebra as the faithful quotient of the action of a quantum group on the tensor power of a certain module, analogous to the construction of the ordinaryq-Schur algebra as a quotient ofU( n).

Item Type: | Article |
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Journal or Publication Title: | Journal of Algebra |

Subjects: | Q Science > QA Mathematics |

Departments: | |

ID Code: | 19393 |

Deposited By: | ep_ss_importer |

Deposited On: | 14 Nov 2008 10:01 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 26 Jul 2012 15:29 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19393 |

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