منابع مشابه
qKZ equation and Alternating Sign Matrices
The integrable loop model with mixed boundary conditions based on the 1-boundary extended Temperley–Lieb algebra with loop weight 1 is considered. The corresponding qKZ equation is introduced and its minimal degree solution described. As a result, the sum of the properly normalized components of the ground state in size L is computed and shown to be equal to the number of Horizontally and Verti...
متن کاملThe Rational Qkz Equation and Shifted Non-symmetric Jack Polynomials
We construct special solutions to the rational quantum KnizhnikZamolodchikov equation associated with the Lie algebra glN . The main ingredient is a special class of the shifted non-symmetric Jack polynomials. It may be regarded as a shifted version of the singular polynomials studied by Dunkl. We conjecture that our solutions contain those obtained as a scaling limit of matrix elements of the ...
متن کاملDifferential Equations Compatible with Boundary Rational Qkz Equation
We give differential equations compatible with the rational qKZ equation with boundary reflection. The total system contains the trigonometric degeneration of the bispectral qKZ equation of type (C n , Cn) which in the case of type GLn was studied by van Meer and Stokman. We construct an integral formula for solutions to our compatible system in a special case.
متن کاملHYPERGEOMETRIC SOLUTIONS OF THE qKZ EQUATION AT LEVEL ZERO
We discuss relations between different integral formulae for solutions of the quantized Knizhnik-Zamolodchikov (qKZ) equation at level zero in the Uq(sl2) case for |q | < 1 . Smirnov type formulae of M. Jimbo et al. are derived from the general approach of A.Varchenko and the author. The consideration is parallel to the qKZ equation in the rational sl2 case done by A.Nakayashiki, S. Pakuliak an...
متن کاملDeterminant Formula for Solutions of the Uq(sln) qKZ Equation at |q | = 1
We construct the hypergeometric solutions for the quantized Knizhnik-Zamolodchikov equation with values in a tensor product of vector representations of Uq(sln) at |q| = 1 and give an explicit formula for the corresponding determinant in terms of the double sine function. Introduction In this paper we study the hypergeometric solutions of the quantized Knizhnik-Zamolodchikov (qKZ) equation with...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2019
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8121/ab3b9e