对称空间量子化的比较：环状Knizhnik-Zamolodchikov方程与Letzter-Kolb余理想
Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik-Zamolodchikov equations and Letzter-Kolb coideals
AI总结：
本文在拟余作用框架下，建立了基于环状KZ方程与Letzter-Kolb余理想的两种对称空间量子化方法的等价性，并推广至带ribbon辫子拟余作用，得到Kohno-Drinfeld型定理，揭示了Hermitian与非Hermitian情形下拟余作用唯一性的差异。
摘要：
我们在拟余作用框架下，建立了紧致型不可约对称空间两种量子化方法之间的等价性，一种基于Enriquez-Etingof环状Knizhnik-Zamolodchikov（KZ）方程，另一种基于Letzter-Kolb余理想。这种等价性可以提升为带ribbon辫子拟余作用的等价性，此时相关的反射算子（K-矩阵）成为量子化的一个可触及不变量。作为应用，我们得到了关于B型辫群表示的Kohno-Drinfeld型定理，该表示由KZ方程的幺正性和Balagović-Kolb泛K-矩阵定义。Hermitian与非Hermitian对称空间的情况有显著差异。特别地，在后一种情形下，拟余作用本质上是唯一的，而在前一种情形下，我们证明存在一个单参数族的互不等价的拟余作用。
英文摘要：
We establish an equivalence between two approaches to quantization of irreducible symmetric spaces of compact type within the framework of quasi-coactions, one based on the Enriquez-Etingof cyclotomic Knizhnik-Zamolodchikov (KZ) equations and the other on the Letzter-Kolb coideals. This equivalence can be upgraded to that of ribbon braided quasi-coactions, and then the associated reflection operators (K-matrices) become a tangible invariant of the quantization. As an application we obtain a Kohno-Drinfeld type theorem on type B braid group representations defined by the monodromy of KZ-equations and by the Balagović-Kolb universal K-matrices. The cases of Hermitian and non-Hermitian symmetric spaces are significantly different. In particular, in the latter case a quasi-coaction is essentially unique, while in the former we show that there is a one-parameter family of mutually nonequivalent quasi-coactions.
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