Ribbon braided module categories, quantum symmetric pairs and Knizhnik-Zamolodchikov equations
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https://hdl.handle.net/10642/7853Utgivelsesdato
2018-11-06Metadata
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Originalversjon
De Commer K, Neshveyev S, Tuset L, Yamashita M. Ribbon braided module categories, quantum symmetric pairs and Knizhnik-Zamolodchikov equations. Communications in Mathematical Physics. 2019;367(3):717-769 https://dx.doi.org/10.1007/s00220-019-03317-7Sammendrag
Let u be a compact semisimple Lie algebra, and σ be a Lie algebra involution of u. Let Repq(u) be the ribbon braided tensor C∗-category of admissible Uq(u)-representations for 0 < q < 1. We introduce three module C∗-categories over Repq(u) starting from the input data (u,σ). 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.