Degeneration of trigonometric dynamical difference equations for quantum loop algebras to trigonometric Casimir equations for Yangians. (English) Zbl 1393.17026
Summary: We show that, under Drinfeld’s degeneration [V. G. Drinfeld, Proc. Int. Congr. Math., Berkeley/Calif. 1986, Vol. 1, 798–820 (1987;Zbl 0667.16003)] of quantum loop algebras to Yangians, the trigonometric dynamical difference equations [P. Etingof and A. Varchenko, Adv. Math. 167, No. 1, 74–127 (2002; Zbl 1033.17010)] for the quantum affine algebra degenerate to the trigonometric Casimir differential equations [V. Toledano Laredo, J. Algebra 329, No. 1, 286–327 (2011; Zbl 1241.17012)] for Yangians.
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 33C80 | Connections of hypergeometric functions with groups and algebras, and related topics |
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