The Affine qSchur algebra
Abstract
We introduce an analogue of the $q$Schur algebra associated to Coxeter systems of type $\hat A_{n1}$. 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 $\hat A_{r1}$, 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 $U(\frak g \frak l_n)$.
 Publication:

eprint arXiv:qalg/9705015
 Pub Date:
 May 1997
 DOI:
 10.48550/arXiv.qalg/9705015
 arXiv:
 arXiv:qalg/9705015
 Bibcode:
 1997q.alg.....5015G
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 29 pages AMSTeX