The Affineq-Schur Algebra
The Affineq-Schur Algebra
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DOI：
10.1006/jabr.1998.7753
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发表时间：
1999-05
影响因子：
0.9
通讯作者：
R. Green
中科院分区：
文献类型：
--
作者：
R. Green
摘要我们引入了一个类似的q -Schur代数与Coxeter系统的类型A n-1。我们给出了这个代数的两个构造。第一种构造将该代数实现为从Ar − 1型仿射Hecke代数产生的某个自同态代数，其中n ≥ r。这推广了Dipper和James定义的原q -Schur代数，新代数包含普通q -Schur代数和仿射Hecke代数作为子代数。使用这种方法，我们可以证明一个双中心化性质。第二个建设实现仿射q -舒尔代数作为忠实的商的行动的量子组上的张量功率的某一模块，类似于建设的普通q -舒尔代数作为商的U（g l n）。
Abstract We introduce an analogue of the q -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 , where n ≥ 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 ( g l n ).