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

Quantum Algebra 2009-11-11 v3 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.math/0605219,
  title  = {Gauss Decomposition of the Yangian Y(gl_{m|n})},
  author = {Lucy Gow},
  journal= {arXiv preprint arXiv:math/0605219},
  year   = {2009}
}

Comments

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