Remarks on $q$-difference opers arising from quantum toroidal algebras
Abstract
We propose a conjectural correspondence between the spectra of the Bethe algebra for the quantum toroidal $\mathfrak{gl}_2$ algebra on relaxed Verma modules, and $q$-hypergeometric opers with apparent singularities. We introduce alongside the notion of apparent singularities for linear $q$-difference operators and discuss some of their properties. We also touch on a generalization to $\mathfrak{gl}_n$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.07265
- arXiv:
- arXiv:2406.07265
- Bibcode:
- 2024arXiv240607265F
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematical Physics
- E-Print:
- Latex, 30 pages