Odd reflections in the Yangian associated with \({\frak gl}(m|n)\)

A. I. Molev

Abstract

The odd reflections is an effective tool in the Lie superalgebra representation theory, as they relate non-conjugate Borel subalgebras. We introduce analogues of the odd reflections for the Yangian \({\rm Y}({\frak gl}_{m|n})\) and use them to produce a transition rule for the parameters of the highest weight modules corresponding to a change of the parity sequence. This leads to a description of the finite-dimensional irreducible representations of the Yangian associated with an arbitrary parity sequence.