Volume 276, Number 3, 799-825, DOI: 10.1007/s00220-007-0349-5

Gauss Decomposition of the Yangian Y(\mathfrakglm|n)Y({\mathfrak{gl}}_{m|n})

Lucy Gow

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Abstract

We describe a Gauss decomposition for the Yangian Y(\mathfrakglm|n)Y({\mathfrak{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)) (for mn) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians Y(\mathfraksln|n)Y({\mathfrak{sl}}_{n|n}) and Y(A(n, n)). We also show that the coefficients of the quantum Berezinian generate the centre of the Yangian Y(\mathfrakglm|n)Y({\mathfrak{gl}}_{m|n}) . This was conjectured by Nazarov in 1991.
Communicated by L. Takhtajan

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