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<p>In this paper we consider an open <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(SL(2,\mathbb {R})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> spin chain, mainly the simplest case of one particle. Eigenfunctions of the model can be constructed using the so-called reflection operator. We obtain several representations of this operator and show its relation to the hypergeometric function. Besides, we prove orthogonality and completeness of one-particle eigenfunctions and connect them to the index hypergeometric transform. Finally, we briefly state the formula for the eigenfunctions in many-particle case. Bibliography: 17 titles.</p>

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REFLECTION OPERATOR AND HYPERGEOMETRY I: \(SL(2,\mathbb {R})\) SPIN CHAIN

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • P. V. Antonenko,
  • N. M. Belousov,
  • S. E. Derkachov,
  • S. M. Khoroshkin

摘要

In this paper we consider an open \(SL(2,\mathbb {R})\) S L ( 2 , R ) spin chain, mainly the simplest case of one particle. Eigenfunctions of the model can be constructed using the so-called reflection operator. We obtain several representations of this operator and show its relation to the hypergeometric function. Besides, we prove orthogonality and completeness of one-particle eigenfunctions and connect them to the index hypergeometric transform. Finally, we briefly state the formula for the eigenfunctions in many-particle case. Bibliography: 17 titles.