Differential equations compatible with boundary rational qKZ equation
Yoshihiro Takeyama
TL;DR
This paper introduces differential equations compatible with the boundary rational qKZ equation, extending previous work on related bispectral equations and providing an integral formula for solutions in a specific case.
Contribution
It constructs differential equations compatible with the boundary rational qKZ equation and offers an integral formula for solutions in a special case, advancing the understanding of these systems.
Findings
Derived differential equations compatible with boundary rational qKZ.
Connected the system to the trigonometric degeneration of bispectral qKZ equations.
Provided an integral formula for solutions in a specific case.
Abstract
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}^{\vee}, C_{n}) which in the case of type GL_{n} was studied by van Meer and Stokman. We construct an integral formula for solutions to our compatible system in a special case.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Mathematical functions and polynomials