Center of the Yangian double in type A
Quantum Algebra
2024-08-20 v2 Mathematical Physics
math.MP
Representation Theory
Abstract
We prove the R-matrix and Drinfeld presentations of the Yangian double in type A are isomorphic. The central elements of the completed Yangian double in type A at the critical level are constructed. The images of these elements under a Harish-Chandra-type homomorphism are calculated by applying a version of the Poincar\'e-Birkhoff-Witt theorem for the R-matrix presentation. These images coincide with the eigenvalues of the central elements in the Wakimoto modules.
Keywords
Cite
@article{arxiv.2207.01712,
title = {Center of the Yangian double in type A},
author = {Yang Fan and Naihuan Jing},
journal= {arXiv preprint arXiv:2207.01712},
year = {2024}
}
Comments
44 pages, no figure. Final version accepted by SCIENCE CHINA Mathematics