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In our paper (Č. Burdík, O. Navrátil. Theor. and Math. Phys. 198 (2019) 1–16) we study the highest weight representations of the RTT–algebra of the \(\text {sp}(4)\) type by the nested algebraic Bethe ansatz. For the constructions we used the RTT–algebra \(\tilde{\mathcal {A}}_2\) . Now we show that our Bethe vectors of this algebra are linearly dependent and the linearly independent vectors can be constructed using Bethe vectors of the RTT–algebra of \(\text {gl}(2)\) type only. In addition, we will present relations from which similar results also follow for RTT–algebras of type \(\text {sp}(2n)\) and \(\text {so}(2n)\) .

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Dependence of Bethe Vectors for RTT–Type Algebra sp(4)

  • 会议论文

  • 发表日期：

    2025年

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  • Čestmír Burdík,
  • Ondřej Navrátil

摘要

In our paper (Č. Burdík, O. Navrátil. Theor. and Math. Phys. 198 (2019) 1–16) we study the highest weight representations of the RTT–algebra of the \(\text {sp}(4)\) type by the nested algebraic Bethe ansatz. For the constructions we used the RTT–algebra \(\tilde{\mathcal {A}}_2\) . Now we show that our Bethe vectors of this algebra are linearly dependent and the linearly independent vectors can be constructed using Bethe vectors of the RTT–algebra of \(\text {gl}(2)\) type only. In addition, we will present relations from which similar results also follow for RTT–algebras of type \(\text {sp}(2n)\) and \(\text {so}(2n)\) .