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}.
Gauss Decomposition of the Yangian Y(gl_{m|n})
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abstract
We describe a Gauss decomposition for the Yangian Y(gl_{m|n}) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebra Y(A(m-1,n-1)) (with m and n not equal) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians Y(sl_{n|n}) and Y(A(n,n)). We also show that the coefficients of the quantum Berezinian generate the centre of Y(gl_{m|n}). This was conjectured by Nazarov in 1991.
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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}.