| Segal－Bargmann－Hall Transform and Geometric Quantization |
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| 引用本文： | 刘卫平,王正栋,胡大鹏. Segal－Bargmann－Hall Transform and Geometric Quantization[J]. 数学进展, 2003, 32(4): 509-511 |
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| 作者姓名： | 刘卫平 王正栋 胡大鹏 |
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| 作者单位： | SchoolofMathematicalScience,PekingUniv.,Beijing,100871,P.R.China |
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| 基金项目： | Supported by the 973 Project Foundation of China(Grant No.TG1999075102)and NSFC |
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| 摘 要： | Using geometric methods, Hall has proved that the Segal-Bargmann transform for a con-nected Lie group K of compact type is an isometric isomorphism [H1] and is unique when Kis simply connected [H7]. Furthermore, Hall considered geometric quantization of T~*(K), K'scotangent bundle [H9]. Using the vertical polarization and a natural Khler polarization obtainedby identifying T~*(K) with the complexified group KC, Hall concluded that the pairing map be-tween the two Hilbert Spaces induced by these two polarizations coincides with the generalizedSegal-Bargmann transform C_t (up to constant).
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| 关 键 词： | Segal－Bargmann－Hall变换 几何量子化 Lie群 等距同构 群表示论 唯一性 连通群 线性映射 |
Segal-Bargmann-Hall Transform and Geometric Quantization |
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| Abstract: | Using geometric methods, Hall has proved that the Segal-Bargmann transform for a con-nected Lie group K of compact type is an isometric isomorphism [H1] and is unique when Kis simply connected [H7]. |
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