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- W4300007237 abstract "We study the q-deformed Knizhnik-Zamolodchikov equation in path representations of the Temperley-Lieb algebras. We consider two types of open boundary conditions, and in both cases we derive factorised expressions for the solutions of the qKZ equation in terms of Baxterised Demazurre-Lusztig operators. These expressions are alternative to known integral solutions for tensor product representations. The factorised expressions reveal the algebraic structure within the qKZ equation, and effectively reduce it to a set of truncation conditions on a single scalar function. The factorised expressions allow for an efficient computation of the full solution once this single scalar function is known. We further study particular polynomial solutions for which certain additional factorised expressions give weighted sums over components of the solution. In the homogeneous limit, we formulate positivity conjectures in the spirit of Di Francesco and Zinn-Justin. We further conjecture relations between weighted sums and individual components of the solutions for larger system sizes." @default.
- W4300007237 created "2022-10-03" @default.
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- W4300007237 date "2007-10-29" @default.
- W4300007237 modified "2023-09-26" @default.
- W4300007237 title "Factorised solutions of Temperley-Lieb $q$KZ equations on a segment" @default.
- W4300007237 doi "https://doi.org/10.48550/arxiv.0710.5362" @default.
- W4300007237 hasPublicationYear "2007" @default.
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