Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model

Abstract

In this paper we construct the quantum spectral curve for the quantum dynamical elliptic gl(n) Gaudin model. We realize it considering a commutative family corresponding to the Felder's elliptic quantum group and taking the appropriate limit. The approach of Manin matrices here suits well to the problem of constructing the generation function of commuting elements which plays an important role in SoV and Langlands concept.

References in corpus (4)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• Quantization of the Gaudin System
• SOS model partition function and the elliptic weight functions
• Classical elliptic current algebras

Cited by in corpus (6)

• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• 1+1 Gaudin Model
• Manin Matrices for Quadratic Algebras
• Dynamical elliptic Bethe algebra, KZB eigenfunctions, and theta-polynomials
• Decomplexification of the Capelli identities and holomorphic factorization
• Quantum Representation Theory and Manin matrices I: finite-dimensional case