On Wronskians and $qq$-systems

Abstract

We discuss the $qq$-systems, the functional form of the Bethe ansatz equations for the twisted Gaudin model from a new geometric point of view. We use a concept of $G$-Wronskians, which are certain meromorphic sections of principal $G$-bundles on the projective line. In this context, the $qq$-system, similar to its difference analog, is realized as the relation between generalized minors of the $G$-Wronskian. We explain the link between $G$-Wronskians and twisted $G$-oper connections, which are the traditional source for the $qq$-systems.

13 pages. arXiv admin note: text overlap with arXiv:2112.02711, arXiv:2108.04184

References in corpus (3)

• Lectures on the integrability of the 6-vertex model
• Quasi-polynomials and the Bethe Ansatz
• Opers on the projective line, flag manifolds and Bethe Ansatz

Cited by in corpus (1)

• Superopers revisited