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arXiv · 2208.08018

On Wronskians and $qq$-systems

Anton M. Zeitlin
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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.

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Anton M. Zeitlin. 2022-08-17. On Wronskians and $qq$-systems. https://doi.org/10.1090/conm%2F791%2F15873

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