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Title:
Opers corresponding to Higher States of the g-Quantum KdV model
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Abstract:
Let g be an untwisted affine Kac-Moody algebra, and consider the g-valued quantum KdV model, obtained from the quantization of the second Poisson bracket for the Drinfeld-Sokolov construction. This is a completely integrable quantum model, solvable via the Bethe Ansatz equations. According to the ODE/IM correspondence (Dorey-Tateo, and Bazhanov-Lukyanov-Zamolodchikov) each solution of the Bethe Ansatz equations can be obtained as the irregular monodromy data of a meromorphic oper. In recent works [1,2], I indeed constructed a solution of the Bethe Ansatz equations - conjecturally the ground-state solution - by considering opers with values in Lg, the Langlands dual Lie algebra of g. In this talk, I will show how to explicitly construct opers corresponding to higher states of the quantum theory, generalising the construction of Bazhanov-Lukyanov-Zamolodchikov for the case
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