Geodesic
Quantization of integrable systems with spectral parameter on a Riemann surface
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 91-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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Given an integrable system defined by a Lax representation with spectral parameter on a Riemann surface, we construct a unitary projective representation of the corresponding Lie algebra of Hamiltonian vector fields by means of operators of covariant derivatives with respect to the Knizhnik–Zamolodchikov connection. It is a Dirac-type prequantization of the integrable system from a physical point of view. Simultaneously, it establishes a correspondence between integrable systems in question and conformal field theories. In the present paper, we focus on systems whose spectral curves possess a holomorphic involution. Examples are presented by Hitchin systems of the types $B_n$, $C_n$, $D_n$, and also of the type $A_n$ on hyperelliptic curves.
Keywords: integrable system, conformal field theory, Knizhnik–Zamolodchikov connection.
Mots-clés : quantization 
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     author = {O. K. Sheinman},
     title = {Quantization of integrable systems with spectral parameter on a {Riemann} surface},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {91--94},
     year = {2020},
     volume = {495},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_495_a18/}
}
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O. K. Sheinman. Quantization of integrable systems with spectral parameter on a Riemann surface. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 91-94. http://geodesic.mathdoc.fr/item/DANMA_2020_495_a18/

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