• Corpus ID: 119611714

# Universal G-oper and Gaudin eigenproblem

@article{Chervov2004UniversalGA,
title={Universal G-oper and Gaudin eigenproblem},
author={Alexander Chervov and Dmitry V. Talalaev},
journal={arXiv: High Energy Physics - Theory},
year={2004}
}
• Published 1 September 2004
• Mathematics
• arXiv: High Energy Physics - Theory
This paper is devoted to the eigenvalue problem for the quantum Gaudin system. We prove the universal correspondence between eigenvalues of Gaudin Hamiltonians and the so-called G-opers without monodromy in general gl(n) case modulo a hypothesys on the analytic properties of the solution of a KZ-type equation. Firstly we explore the quantum analog of the characteristic polynomial which is a differential operator in a variable $u$ with the coefficients in U(gl(n))^{\otimes N}. We will call it…
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Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra $${U(\mathfrak {g})}$$ of a semisimple Lie algebra $${\mathfrak • Mathematics • 2007 Let M be the tensor product of finite-dimensional polynomial evaluation Y (gl N )- modules. Consider the universal difference operator D = N P k=0 ( 1) k Tk(u)e k@u whose coef- ficients Tk(u) : M ! M • Mathematics • 2007 The first part of the present paper is devoted to a systematic construction of continuous-time finite-dimensional integrable systems arising from the rational$${\mathfrak su(2)}$$Gaudin model • Mathematics • 2007 In this paper we study properties of Lax and transfer matrices associated with quantum integrable systems. Our point of view stems from the fact that their elements satisfy special commutation ## References SHOWING 1-10 OF 24 REFERENCES This is a review of our previous works [FFR, F1, F3] (some of them joint with B. Feigin and N. Reshetikhin) on the Gaudin model and opers. We define a commutative subalgebra in the tensor power of • Mathematics • 1995 We adapt Hitchin's integrable systems to the case of a punctured curve. In the case of \CC P^{1} and SL_{n}-bundles, they are equivalent to systems studied by Garnier. The corresponding quantum • Mathematics • 1993 AbstractDarboux coordinates are constructed on rational coadjoint orbits of the positive frequency part$$\tilde{\mathfrak{g}}^+$$of loop algebras. These are given by the values of the spectral • Mathematics • 2003 In this paper, we discuss the bi-Hamiltonian formulation of the (rational XXX) Gaudin models of spin–spin interaction, generalized to the case of sl(r)-valued 'spins'. We only consider the classical In this article we exploit the known commutative family in Y(gl(n)) - the Bethe subalgebra - and its special limit to construct quantization of the Gaudin integrable system. We give explicit • Mathematics • 1988 AbstractA moment map$$\tilde J_r :M_A \to (\widetilde{gl(r)}^ + )^*$$is constructed from the Poisson manifold ℳA of rank-r perturbations of a fixedN×N matrixA to the dual$$(\widetilde{gl(r)}^ +
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