Quantum Sugawara operators in type $A$
Quantum Algebra
2024-09-02 v1 Mathematical Physics
math.MP
Representation Theory
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.
Cite
@article{arxiv.2212.11435,
title = {Quantum Sugawara operators in type $A$},
author = {Naihuan Jing and Ming Liu and Alexander Molev},
journal= {arXiv preprint arXiv:2212.11435},
year = {2024}
}
Comments
23 pages, extending the construction of arXiv:1505.03667 to arbitrary Young diagrams