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.

arXiv comment27 pages. Small corrections have been made throughout. Some new results have been added

References in corpus (9)

• Parabolic presentations of the Yangian Y(gl_n)
• The gl(M|N) Super Yangian and Its Finite Dimensional Representations
• Defining Relations for Lie Superalgebras with Cartan matrix
• Yangian Symmetry in D=4 Superconformal Yang-Mills Theory
• $gl(n|m)$ color Calogero-Sutherland models and Super Yangian Algebra
• Hopf structure of the Yangian Y(sl_n) in the Drinfel'd realisation
• Lax pair and super-Yangian symmetry of the non-linear super-Schrödinger equation
• The Algebraic Structure of the $gl(n|m)$ Color Calogero-Sutherland Models
• Super Yangian Double $DY(gl(1|1))$ and Its Gauss Decomposition

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