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Are there some references which write presentations of quantum general linear groups explicitly? For example, what are generators and relations for $U_q(gl_2)$? Thank you very much.

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    $\begingroup$ Don't most sources define $U_q\left(\mathfrak{gl}_n\right)$ via generators and relations? I thought doing it in any other way would be way too difficult. $\endgroup$
    – darij grinberg
    Commented Aug 2, 2017 at 15:07
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    $\begingroup$ Specifically for $U_q\left(\mathfrak{gl}_2\right)$, a neat nonstandard presentation was found by Ito, Terwilliger and Weng: arxiv.org/abs/math/0507477v1 $\endgroup$
    – darij grinberg
    Commented Aug 2, 2017 at 15:08

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We can find a presentation in NONCOMMUTATIVE SYMMETRIC FUNCTIONS V: A DEGENERATE VERSION OF $U_q(gl_N)$.

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