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Title:
Homomorphisms between different quantum toroidal and affine Yangian algebras
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Abstract:
In the recent work of Gautam and Toledano Laredo, a new relation between the quantum affine algebra Uq(Lg) and the Yangian Y~(g) of a simple Lie algebra g was established by constructing an isomorphism between completions of those two algebras, where q = exp(~) and ~ is viewed as a formal parameter. It turns out that their approach can be generalized to construct homomorphisms from the quantum toroidal algebra of slm (which depends on two parameters q1, q2) to a completion of the affine Yangian of slmn (which depends on two parameters ~1, ~2), where q1 = ω exp(~1), q2 = exp(~2) and ω is an mn-th root of unity.
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