Ribbon Braided Module Categories, Quantum Symmetric Pairs and Knizhnik?Zamolodchikov Equations
Ribbon Braided Module Categories, Quantum Symmetric Pairs and Knizhnik?Zamolodchikov Equations
复制标题
带状编织模块类别、量子对称对和 Knizhnik?Zamolodchikov 方程
DOI：
10.1007/s00220-019-03317-7
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发表时间：
2019
影响因子：
2.4
通讯作者：
Yamashita Makoto
中科院分区：
文献类型：
--
作者：
De Commer Kenny;Neshveyev Sergey;Tuset Lars;Yamashita Makoto
设为紧半单李代数，且为的李代数对合。令带状编织张量C*- 0 <q< 1时容许表示的范畴。我们从输入数据出发，引入了三个模块C*类。第一种结构是基于2-分环kz方程的理论。第二种结构使用了由G. Letzter提出的量子对称对的概念。第三种结构使用了一种变化的德林菲尔德扭转。在所有三种情况下，模C*-范畴都是A. brochier意义上的带状扭曲-这在第一种情况下基本上是由于B. Enriquez，在第二种情况下由S. Kolb证明，并且与J. Donin， P. Kulish和A. Mudrov在第三种情况下的工作密切相关。我们提出了一个关于这些带状捻编模C*-类的等价性的猜想，并在秩一情况下予以证实。
Letbe a compact semisimple Lie algebra, andbe a Lie algebra involution of. Letbe the ribbon braided tensor C*-category of admissible-representations for 0 <q< 1. We introduce three module C*-categories overstarting from the input data. The first construction is based on the theory of 2-cyclotomic KZ-equations. The second construction uses the notion of quantum symmetric pair as developed by G. Letzter. The third construction uses a variation of Drinfeld twisting. In all three cases the module C*-category is ribbon twist-braided in the sense of A. Brochier—this is essentially due to B. Enriquez in the first case, is proved by S. Kolb in the second case, and is closely related to work of J. Donin, P. Kulish, and A. Mudrov in the third case. We formulate a conjecture concerning equivalence of these ribbon twist-braided module C*-categories, and confirm it in the rank one case.