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In this chapter, we give the explicit star product giving the deformation quantization with separation of variables on the complex Grassmannian \(G_{2,4}(\mathbb {C})\) by using the construction method proposed by Hara and one of the authors (A. S.). We show that for \(G_{2,4}(\mathbb {C})\) , the general terms of the recurrence relations given by Hara-S. can be determined explicitly. From the obtained general terms, we provide the star product on \(G_{2,4}(\mathbb {C})\) explicitly.

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Explicit Formulae for Deformation Quantization with Separation of Variables of \(G_{2,4}(\mathbb {C})\)

  • 会议论文

  • 发表日期：

    2025年

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  • Taika Okuda,
  • Akifumi Sako

摘要

In this chapter, we give the explicit star product giving the deformation quantization with separation of variables on the complex Grassmannian \(G_{2,4}(\mathbb {C})\) by using the construction method proposed by Hara and one of the authors (A. S.). We show that for \(G_{2,4}(\mathbb {C})\) , the general terms of the recurrence relations given by Hara-S. can be determined explicitly. From the obtained general terms, we provide the star product on \(G_{2,4}(\mathbb {C})\) explicitly.