Center of the Yangian double in type A

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.

arXiv comment44 pages, no figure. Final version accepted by SCIENCE CHINA Mathematics

References in corpus (7)

• The Quantum Double in Integrable Quantum Field Theory
• Infinite Quantum Group Symmetry of Fields in Massive 2D Quantum Field Theory
• Feigin-Frenkel center in types B, C and D
• Center of the quantum affine vertex algebra in type A
• Higher Sugawara operators for the quantum affine algebras of type A
• Hopf structure of the Yangian Y(sl_n) in the Drinfel'd realisation
• Yangian doubles of classical types and their vertex representations

Cited by in corpus (2)

• A note on the quantum Berezinian for the double Yangian of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$
• Semi-infinite construction for the double Yangian of type $A_1^{(1)}$