Year: 2024
Type: article
Abstract: We consider the classification problem for finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras $$\mathfrak {osp}_{2n|2m}$$ osp 2 n | 2 m with $$n\geqslant 2$$ n ⩾ 2 . We give necessary conditions for an irreducible highest weight representation to be finite-dimensional. We conjecture that these conditions are also sufficient and prove the conjecture for a class of representations with linear highest weights. The arguments are based on a new type of odd reflections for the Yangian associated with $$\mathfrak {osp}_{2|2}$$ osp 2 | 2 . In the Appendix, we construct an isomorphism between the Yangians associated with the Lie superalgebras $$\mathfrak {osp}_{2|2}$$ osp 2 | 2 and $$\mathfrak {gl}_{1|2}$$ gl 1 | 2 .
Author: A. I. Molev
Institution: The University of Sydney
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4405864800