Odd reflections in the Yangian associated with ${\frak gl}(mn)$
Abstract
The odd reflections is an effective tool in the Lie superalgebra representation theory, as they relate nonconjugate Borel subalgebras. We introduce analogues of the odd reflections for the Yangian ${\rm Y}({\frak gl}_{mn})$ 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 finitedimensional irreducible representations of the Yangian associated with an arbitrary parity sequence.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.09462
 Bibcode:
 2021arXiv210909462M
 Keywords:

 Mathematics  Representation Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra
 EPrint:
 14 pages