Quantum Sugawara operators in type $A$

TL;DR

This paper explicitly constructs quantum Sugawara operators for type A affine algebras, linking them to Hecke algebra idempotents and Young diagrams, and analyzes their eigenvalues in q-deformed modules.

Contribution

It provides a new explicit construction of quantum Sugawara operators associated with Young diagrams, extending previous work to more general diagrams.

Findings

Explicit formulas for quantum Sugawara operators.

Identification of Harish-Chandra images with eigenvalues.

Extension of previous constructions to general Young diagrams.

Abstract

We construct Sugawara operators for the quantum affine algebra of type $A$ 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 $q$-deformed Wakimoto modules.