q-SCHUR ALGEBRAS CORRESPONDING TO HECKE ALGEBRAS OF TYPE B
q-SCHUR ALGEBRAS CORRESPONDING TO HECKE ALGEBRAS OF TYPE B
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DOI：
10.1007/s00031-020-09628-7
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发表时间：
2020-10
影响因子：
0.7
通讯作者：
Chun-Ju Lai;Daniel K. Nakano;Ziqing Xiang
中科院分区：
文献类型：
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作者：
Chun-Ju Lai;Daniel K. Nakano;Ziqing Xiang
本文研究了B型q-Schur代数，它是用A型量子群的余理想子代数构造的.给出了一个坐标代数型的构造，它允许我们将这些类Schur代数实现为某些分次余代数的第d分次分支的集合.在适当的条件下，证明了一个同构定理，证明了表示论可约化为A型q-Schur代数.这使作者能够解决这些代数的胞腔性，拟遗传性和表示类型的问题。后来证明了这些代数实现了B型Hecke代数的1-忠实拟遗传覆盖。作为进一步的结果，作者证明了这些代数是Morita等价于B型Weyl群的有理Cherednik代数的范畴。𝒪特别地，我们引入了一个Schur型函子，它标识了B Knizhnik-Zamolodchikov型函子。
In this paper the authors investigate theq-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type Α. The authors present a coordinate algebra type construction that allows us to realize theseq-Schur algebras as the duals of thedth graded components of certain graded coalgebras. Under suitable conditions an isomorphism theorem is proved that demonstrates that the representation theory reduces to theq-Schur algebra of type Α. This enables the authors to address the questions of cellularity, quasi-hereditariness and representation type of these algebras. Later it is shown that these algebras realize the 1-faithful quasi hereditary covers of the Hecke algebras of type Β. As a further consequence, the authors demonstrate that these algebras are Morita equivalent to the category 𝒪 for rational Cherednik algebras for the Weyl group of type Β. In particular, we have introduced a Schur-type functor that identifies the type Β Knizhnik–Zamolodchikov functor.