English

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

Representation Theory 2022-01-14 v3 Mathematical Physics math.MP Quantum Algebra

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 Y(glmn){\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.

Keywords

Cite

@article{arxiv.2109.09462,
  title  = {Odd reflections in the Yangian associated with ${\frak gl}(m|n)$},
  author = {A. I. Molev},
  journal= {arXiv preprint arXiv:2109.09462},
  year   = {2022}
}

Comments

14 pages, minor changes