Schur–Weyl duality for higher levels
Schur–Weyl duality for higher levels
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DOI：
10.1007/s00029-008-0059-7
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发表时间：
2006-05
期刊：
影响因子：
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通讯作者：
Jonathan Brundan;A. Kleshchev
中科院分区：
文献类型：
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作者：
Jonathan Brundan;A. Kleshchev
我们将Schur-Weyl对偶推广到任意级≥[1]，恢复了对称线性群和一般线性群之间的经典对偶。一般而言，对于A型∞的根系统，对称群被退化的割圆Hecke代数代替，该代数被超参数化的水平控制权所代替。作为应用，我们证明了Dipper，James和Mathas构造的割圆Hecke代数的拟遗传覆盖的退化类似于一般线性李代数的某些抛物范畴块的Morita等价。
We extend Schur–Weyl duality to an arbitrary levell≥ 1, level one recovering the classical duality between the symmetric and general linear groups. In general, the symmetric group is replaced by the degenerate cyclotomic Hecke algebra overparametrized by a dominant weight of levellfor the root system of type A∞. As an application, we prove that the degenerate analogue of the quasi-hereditary cover of the cyclotomic Hecke algebra constructed by Dipper, James and Mathas is Morita equivalent to certain blocks of parabolic categoryfor the general linear Lie algebra.