The Affine q-Schur algebra
| dc.creator | Green, R. M. | |
| dc.date | 1997-05-23 | |
| dc.date | 1998-10-13 | |
| dc.date.accessioned | 2026-07-07T09:08:47Z | |
| dc.date.available | 2026-07-07T09:08:47Z | |
| dc.description | We introduce an analogue of the $q$-Schur algebra associated to Coxeter systems of type $\hat A_{n-1}$. 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 $\hat A_{r-1}$, where $n \geq r$. This generalizes the original $q$-Schur algebra as defined by Dipper and James, and the new algebra contains the ordinary $q$-Schur algebra and the affine Hecke algebra as subalgebras. Using this approach we can prove a double centralizer property. The second construction realizes the affine $q$-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 ordinary $q$-Schur algebra as a quotient of $U(\frak g \frak l_n)$. | |
| dc.description | 29 pages AMSTeX; 1 eps figure | |
| dc.identifier | https://arxiv.org/abs/q-alg/9705015 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9705015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150846 | |
| dc.subject | Quantum Algebra | |
| dc.title | The Affine q-Schur algebra | |
| dc.type | text |