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

Abstract

The odd reflections are 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 \( \mathrm{Y}(\mathfrak {gl}_{m|n})\) 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.