$Q\tilde{Q}$-systems for twisted quantum affine algebras

Abstract

We establish the $Q\tilde{Q}$-systems for the twisted quantum affine algebras that were conjectured in arXiv:1606.05301. We develop the representation theory of Borel subalgebra of twisted quantum affine algebras and we construct their prefundamental representations. We also propose a general conjecture on the relations between twisted and non-twisted types. We prove this conjecture for some particular classes of representations, including prefundamental representations.

arXiv comment39 pages

References in corpus (12)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• The ODE/IM Correspondence
• Baxter's Relations and Spectra of Quantum Integrable Models
• Asymptotic representations and Drinfeld rational fractions
• Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case
• Bethe Ansatz and the Spectral Theory of affine Lie algebra--valued connections II. The non simply--laced case
• Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
• Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras
• Simple tensor products
• Finite type modules and Bethe ansatz equations

Cited by in corpus (3)

• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Feigin-Frenkel-Hernandez Opers and the QQ-system
• Theta series for quantum loop algebras and Yangians