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

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 $\mathrm{Y}({\mathfrak{g}\mathfrak{l}}_{m|n})$ 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.