Center of the Yangian double in type A
arXiv:2207.01712 · doi:10.1007/s11425-022-2142-9
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 Poincaré-Birkhoff-Witt theorem for the R-matrix presentation. These images coincide with the eigenvalues of the central elements in the Wakimoto modules.
44 pages, no figure. Final version accepted by SCIENCE CHINA Mathematics