Representations of the Yangian of a Lie superalgebra of type $ A(m,n)$

Odd reflections in the Yangian associated with ${\frak gl}(m|n)$

“…However, they are sufficient in the case of the standard parity sequence s = s st . The next theorem, whose proof we outline below, is due to Zhang [22]; see also [17]. We will write Y(gl m|n ) for the Yangian associated with the sequence s st = 0 .…”

“…As this relies on such conditions for the standard parity sequence, we will give a brief review (in Section 3) of the classification results for the finite-dimensional irreducible representations of the Yangian Y(gl m|n ) following [21] and [22]; cf. [17] where an approach based on the Drinfeld presentation was used.…”

Isomorphism between super Yangian and quantum loop superalgebra. I

“…It should also mention the works [9], [10], in which this approach is significantly strengthened and used to investigate the connection between categories of representations of Yangians and quantum loop algebras. Actually, such an investigation is our goal, and this work is the first step in this direction (see also the papers [18], [22], devoted to the representations of the special linear Lie superalgebra of the Yangian). To simplify the presentation, we also omitted the proofs of some auxiliary assertions, which we are going to publish in the second part of this paper.…”

Drinfeld Yangian of the queer Lie superalgebra. I

“…We note that simplifying the proof of the theorem on isomorphism from section 5, we somewhat changed the current system of generators in this paper in comparison with the papers [22], [23], [26] which led to a somewhat simpler and more natural form of defining relations.…”