Equivalences between three presentations of orthogonal and symplectic Yangians

TY - JOUR

T1 - Equivalences between three presentations of orthogonal and symplectic Yangians

AU - Guay, Nicolas

AU - Regelskis, Vidas

AU - Wendlandt, Curtis

N1 - © Springer Nature B.V. 2018. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

PY - 2018/6/21

Y1 - 2018/6/21

N2 - We prove the equivalence of two presentations of the Yangian $Y(\mathfrak{g})$ of a simple Lie algebra $\mathfrak{g}$ and we also show the equivalence with a third presentation when $\mathfrak{g}$ is either an orthogonal or a symplectic Lie algebra. As an application, we obtain an explicit correspondence between two versions of the classification theorem of finite-dimensional irreducible modules for orthogonal and symplectic Yangians.

AB - We prove the equivalence of two presentations of the Yangian $Y(\mathfrak{g})$ of a simple Lie algebra $\mathfrak{g}$ and we also show the equivalence with a third presentation when $\mathfrak{g}$ is either an orthogonal or a symplectic Lie algebra. As an application, we obtain an explicit correspondence between two versions of the classification theorem of finite-dimensional irreducible modules for orthogonal and symplectic Yangians.

KW - math.RT

KW - math.QA

UR - http://www.scopus.com/inward/record.url?scp=85048742311&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1706.05176

U2 - 10.1007/s11005-018-1108-6

DO - 10.1007/s11005-018-1108-6

M3 - Article

SN - 1573-0530

SP - 1

EP - 53

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

ER -