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

TL;DR

This paper introduces odd reflection analogues for the Yangian of gl(m|n), enabling a comprehensive description of finite-dimensional irreducible representations across different parity sequences.

Contribution

It develops a new framework of odd reflections for Yangians, extending their use to classify finite-dimensional irreducible modules with arbitrary parity sequences.

Findings

Established transition rules for highest weight parameters.

Provided a classification of finite-dimensional irreducible representations.

Extended odd reflection techniques to Yangian structures.

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 ${\rm Y}({\frak gl}_{m|n})$ 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.