The authors extend the Etingof-Kazhdan quantum vertex algebra construction and the critical-level central element construction from the double Yangian of gl_M to the Lie superalgebra gl_{M|N}.
Odd reflections in the Yangian associated with ${\frak gl}(m|n)$
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abstract
The odd reflections are an effective tool in the Lie superalgebra representation theory, as they relate non-conjugate Borel subalgebras. We introduce analogues of the odd reflections for the Yangian ${\rm Y}({\frak gl}_{m|n})$ and use them to produce a transition rule for the parameters of the highest weight modules corresponding to a change of the parity sequence. This leads to a description of the finite-dimensional irreducible representations of the Yangian associated with an arbitrary parity sequence.
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Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{M|N}$, II: Quantum currents
The authors extend the Etingof-Kazhdan quantum vertex algebra construction and the critical-level central element construction from the double Yangian of gl_M to the Lie superalgebra gl_{M|N}.