Gauss Decomposition of the Yangian Y(gl_{m|n})

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.