Asymptotic Solutions to the Knizhnik-Zamolodchikov Equation and Crystal Base

Abstract

The Knizhnik-Zamolodchikov equation associated with $s{\ell }_2$ is considered. The transition functions between asymptotic solutions to the Knizhnik-Zamolodchikov equation are described. A connection between asymptotic solutions and the crystal base in the tensor product of modules over the quantum group $U_{q}s{\ell }_2$ is established, in particular, a correspondence between the Bethe vectors of the Gaudin model of an inhomogenious magnetic chain and the $\mathbb{Q}-$basis of the crystal base.

arXiv comment43 pages, amstex

References in corpus (3)

• Gaudin Model, Bethe Ansatz and Critical Level
• Quasiclassical asymptotics of solutions to the KZ equations
• Off-Shell Bethe Ansatz Equation and N-point Correlators in the SU(2) WZNW Theory

Cited by in corpus (10)

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• Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets
• Crystals and monodromy of Bethe vectors
• The Hubbard chain: Lieb-Wu equations and norm of the eigenfunctions
• Cyclotomic Gaudin models: construction and Bethe ansatz
• The Drinfeld-Kohno theorem for the superalgebra $gl(1|1)$
• About the Rationality of the Knizhnik-Zamolodchikov Equation Solution
• On inner product in modular tensor categories. II. Inner product on conformal blocks and affine inner product identities
• Canonical basis and homology of local systems