# quantum affine $gl_2$

There are many sources of the relations and Hopf algebra structure of quantum affine $$sl_2$$ as a deformed enveloping algebra. However, for an application to integrable systems I need to look at quantum affine $$gl_2$$, not $$sl_2$$. Also it would be really good to see how this fits into the Drinfeld realisation with the $$h_r$$ and $$x^\pm_r$$ for $$r\in\mathbb{Z}$$. I would be very grateful if someone could point me in the right direction.

I guess you mean the following presentation in terms of generators and relations: The excerpt is from:

• Evaluation modules for quantum toroidal $${\mathfrak{gl}}_n$$ algebras, arXiv:1709.01592v4 [math.QA], p.3

I think the OP might also find some interest at:

You can also see (both Jimbo's and Drinfeld's presentation of the quantum affine $$sl_2$$) at:

• Many thanks for that! Is there any particular reason why the degree operator is left out? I assume that it could be put back in... – Edwin Beggs May 20 at 7:31
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