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Completeness of Bethe Ansatz for Gaudin Models with gl(1|1) Symmetry and Diagonal Twists
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Version 1
: Received: 24 November 2022 / Approved: 28 November 2022 / Online: 28 November 2022 (08:01:42 CET)
A peer-reviewed article of this Preprint also exists.
Lu, K. Completeness of Bethe Ansatz for Gaudin Models with gl(1|1) Symmetry and Diagonal Twists. Symmetry 2023, 15, 9. Lu, K. Completeness of Bethe Ansatz for Gaudin Models with gl(1|1) Symmetry and Diagonal Twists. Symmetry 2023, 15, 9.
Abstract
We study the Gaudin models with gl(1|1) symmetry that are twisted by a diagonal matrix and defined on tensor products of polynomial evaluation gl(1|1)[t]-modules, extending all the results of to the twisted case. Namely, we give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation gl(1|1)[t]-modules and show that there exists a bijection between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the highest weights and evaluation parameters. In particular, our result implies that each common eigenspace of the algebra of Hamiltonians has dimension one. We also give dimensions of the generalized eigenspaces.
Keywords
Gaudin models; Lie superalgebras; Bethe ansatz; Pseudo-differential operators; Berezinian
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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