Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 040, 14 pages      arXiv:1505.03619      https://doi.org/10.3842/SIGMA.2015.040
Contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet

From Twisted Quantum Loop Algebras to Twisted Yangians

Patrick Conner a and Nicolas Guay b
a) Science Department, Red Deer College, Red Deer, Alberta T4N 5H5, Canada
b) Department of Mathematical and Statistical Sciences, University of Alberta, CAB 632, Edmonton, Alberta T6G 2G1, Canada

Received January 30, 2015, in final form May 01, 2015; Published online May 14, 2015

Abstract
We prove how the Yangian of $\mathfrak{gl}_N$ in its RTT presentation and Olshanski's twisted Yangians for the orthogonal and symplectic Lie algebras can be obtained by a degeneration process from the corresponding quantum loop algebra and some of its twisted analogues.

Key words: twisted Yangians; twisted quantum loop algebras; degeneration; RTT-presentation.

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