The trigonometric Casimir connection of a simple Lie algebra

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• 关键词：Trigonometric connection ; Casimir connection ; Yangian ; Monodromy ; Quantum Weyl groups ; Bispectrality
• 刊名：Journal of Algebra
• 出版年：2011
• 出版时间：1 March 2011
• 年：2011
• 卷：329
• 期：1
• 页码：286-327
• 全文大小：414 K

文摘

Let be a complex, semisimple Lie algebra, G the corresponding simply-connected Lie group and HG a maximal torus. We construct a flat connection on H with logarithmic singularities on the root hypertori and values in the Yangian of . By analogy with the rational Casimir connection of , we conjecture that the monodromy of this trigonometric connection is described by the quantum Weyl group operators of the quantum loop algebra .