In this paper the authors investigate the q-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 these q-Schur algebras as the duals of the dth graded components of certain graded coalgebras. Under suitable conditions an isomorphism theorem is proved that demonstrates that the representation theory reduces to the q-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.

在本文中，作者研究了B 型q -Schur 代数，这些代数是使用 α 型量子群的共理想子代数构建的。作者提出了一种坐标代数类型的构造，它允许我们将这些q -Schur 代数实现为某些分级余代数的第d分级分量的对偶。在适当的条件下，证明了一个同构定理，证明了表示论可以简化为q- α 类型的 Schur 代数。这使作者能够解决这些代数的细胞性、准遗传性和表示类型的问题。后来证明这些代数实现了 Β 型 Hecke 代数的 1-忠实准遗传覆盖。作为进一步的结果，作者证明这些代数是 Morita 等价于类型 Β 的 Weyl 群的有理 Cherednik 代数的范畴 𝒪。特别是，我们引入了一个 Schur 型函子，它识别类型 Β Knizhnik-Zamolodchikov 函子。