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A Recent Look at the Quantum Berezinian in the Yangian Y(gl_{m|n})

Lucy Gow
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Abstract

Brundan and Kleshchev recently introduced a new family of presentations of the Yangian Y(gl_n) associated to the general linear Lie algebra gl_n, and thus provided a fresh approach to its study. In this article, we show how some of their ideas can be fruitfully extended to consider the Yangian Y(gl_{m|n}) associated to the Lie superalgebra gl_{m|n}. In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central.

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Lucy Gow. 2006-01-20. A Recent Look at the Quantum Berezinian in the Yangian Y(gl_{m|n}). https://arxiv.org/abs/math/0501041

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