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 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