Asymptotic Solutions to the Quantized Knizhnik-Zamolodchikov Equation and Bethe Vectors

Abstract

Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation associated with ${\mathfrak{gl}}_{N+1}$ are constructed. The leading term of an asymptotic solution is the Bethe vector -- an eigenvector of the transfer-matrix of a quantum spin chain model. We show that the norm of the Bethe vector is equal to the product of the Hessian of a suitable function and an explicitly written rational function. This formula is an analogue of the Gaudin-Korepin formula for the norm of the Bethe vector. It is shown that, generically, the Bethe vectors form a base for the ${\mathfrak{gl}}_2$ case.

arXiv comment30 pages. Minor misprints are corrected

Cited by in corpus (1)

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