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 E_{τ,h}(gl_n) 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.

Keywords

• Manin matrices
• L-operators
• elliptic Felder R-matrix
• Gaudin models