Remarks on q-difference opers arising from quantum toroidal algebras

2024/06/11 by Boris Feigin, Feigin, B., M. Jimbo +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2406.07265

Abstract

We propose a conjectural correspondence between the spectra of the Bethe algebra for the quantum toroidal \mathfrakgl₂ 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 \mathfrakgl_n.

Related

• Toroidal actions on level 1 modules of U_q(sl_n)
• Higgsing qq-character and irreducibility
• Quantum toroidal gl(1) and Bethe ansatz
• (t,q) Q-systems, DAHA and quantum toroidal algebras via generalized\n Macdonald operators
• Combinatorial bases in quantum toroidal \mathfrakgl₂ modules