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Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we construct the quantum spectral curve for the quantum dynamical elliptic $\mathfrak{gl}_n$ Gaudin model. We realize it considering a commutative family corresponding to the Felder's elliptic quantum group $E_{\tau,\hbar}(\mathfrak{gl}_n)$ 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. 
@article{SIGMA_2009_5_a109,
     author = {Vladimir Rubtsov and Alexey Silantyev and Dmitri Talalaev},
     title = {Manin {Matrices,} {Quantum} {Elliptic} {Commutative} {Families} and {Characteristic} {Polynomial} of {Elliptic} {Gaudin} {Model}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2009},
     volume = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a109/}
}
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Vladimir Rubtsov; Alexey Silantyev; Dmitri Talalaev. Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a109/

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