Quantum Sugawara operators in type
arXiv:2212.11435 · doi:10.1016/j.aim.2024.109907
Abstract
We construct Sugawara operators for the quantum affine algebra of type in an explicit form. The operators are associated with primitive idempotents of the Hecke algebra and parameterized by Young diagrams. This generalizes a previous construction (2016) where one-column diagrams were considered. We calculate the Harish-Chandra images of the Sugawara operators and identify them with the eigenvalues of the operators acting in the -deformed Wakimoto modules.
23 pages, extending the construction of arXiv:1505.03667 to arbitrary Young diagrams