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

Lucy Gow

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.

Keywords: Yangian, quasideterminants, Lie superalgebras.

AMS Subject Classification: Primary 17B37.