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The affine q-Schur algebra.

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The affine q-Schur algebra. / Green, R. M.
In: Journal of Algebra, Vol. 215, No. 2, 15.05.1999, p. 379-411.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Green, RM 1999, 'The affine q-Schur algebra.', Journal of Algebra, vol. 215, no. 2, pp. 379-411. https://doi.org/10.1006/jabr.1998.7753

APA

Green, R. M. (1999). The affine q-Schur algebra. Journal of Algebra, 215(2), 379-411. https://doi.org/10.1006/jabr.1998.7753

Vancouver

Green RM. The affine q-Schur algebra. Journal of Algebra. 1999 May 15;215(2):379-411. doi: 10.1006/jabr.1998.7753

Author

Green, R. M. / The affine q-Schur algebra. In: Journal of Algebra. 1999 ; Vol. 215, No. 2. pp. 379-411.

Bibtex

@article{2549b8ccbd4f4a0a9e23aa1eea6cd9c4,
title = "The affine q-Schur algebra.",
abstract = "We introduce an analogue of theq-Schur algebra associated to Coxeter systems of type{\'A}n − 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 type{\'A}r − 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).",
author = "Green, {R. M.}",
year = "1999",
month = may,
day = "15",
doi = "10.1006/jabr.1998.7753",
language = "English",
volume = "215",
pages = "379--411",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "ELSEVIER ACADEMIC PRESS INC",
number = "2",

}

RIS

TY - JOUR

T1 - The affine q-Schur algebra.

AU - Green, R. M.

PY - 1999/5/15

Y1 - 1999/5/15

N2 - 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).

AB - 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).

U2 - 10.1006/jabr.1998.7753

DO - 10.1006/jabr.1998.7753

M3 - Journal article

VL - 215

SP - 379

EP - 411

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -