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Asymptotic Solutions to the Quantized Knizhnik-Zamolodchikov Equation and Bethe Vectors
Vitaly Tarasov, Alexander Varchenko
Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation associated with are constructed. The leading term of an asymptotic solution is the Bethe vec…
On Solutions to the Twisted Yang-Baxter equation
Vitaly Tarasov
Solutions to the twisted Yang-Baxter equation, arising from intertwiners for cyclic representations of are described via two coupled the lattice current algeb…
Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation
Vitaly Tarasov, Alexander Varchenko
The quantized Knizhnik-Zamolodchikov equations associated with the trigonometric R-matrix or the rational R-matrix of the A-type are considered. Jackson integral representations fo…
Yangians and Gelfand-Zetlin bases
M. Nazarov, Vitaly Tarasov
We establish a relationship between the modern theory of Yangians and the classical construction of the Gelfand-Zetlin bases for the complex Lie algebra $\gn$. Our approach allows…
Cyclic monodromy matrices for sl(n) trigonometric R-matrices
Vitaly Tarasov
The algebra of monodromy matrices for sl(n) trigonometric R-matrices is studied. It is shown that a generic finite-dimensional polynomial irreducible representation of this algebra…