新疆大学数学与系统科学学院,新疆 乌鲁木齐 830017
金四海(1997年生),男;研究方向:李群表示论;E-mail:jinsihai@stu.xju.edu.cn
范兴亚(1986年生),男;研究方向:李群表示论;E-mail:fanxingya@xju.edu.cn
纸质出版日期:2024-01-25,
网络出版日期:2023-11-15,
收稿日期:2022-10-19,
录用日期:2023-02-20
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金四海,范兴亚.仿射对称空间SU(1,2)/SO(1,2)上的Plancherel定理[J].中山大学学报(自然科学版)(中英文),2024,63(01):173-180.
JIN Sihai,FAN Xingya.Plancherel theorem for the affine symmetric space SU(1,2)/SO(1,2)[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(01):173-180.
金四海,范兴亚.仿射对称空间SU(1,2)/SO(1,2)上的Plancherel定理[J].中山大学学报(自然科学版)(中英文),2024,63(01):173-180. DOI: 10.13471/j.cnki.acta.snus.2022A091.
JIN Sihai,FAN Xingya.Plancherel theorem for the affine symmetric space SU(1,2)/SO(1,2)[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(01):173-180. DOI: 10.13471/j.cnki.acta.snus.2022A091.
研究了Hilbert空间
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上酉表示的不可约分解,其中
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是Hermitian型仿射对称空间,
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是群
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作用在
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1.94733346
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上不变的Haar测度. 利用
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11.09133339
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不变的分布函数,具体的构造了缠结算子,进而得到了
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上的离散序列表示. 在此基础上,结合离散序列表示的正交补部分,证明了
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上的Plancherel公式.
The irreducible decomposition of unitary representations is investigated on the Hilbert space
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, where
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2</mn><mo stretchy="false">)</mo></math>
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33.44333267
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, and
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denotes an
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-invariant Haar measure on
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By using the
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-invariant distribution functions, the intertwining operators is constructed concretely, and then the discrete series representations on
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are obtained. On this basis, combined with the orthogonal complement parts of the discrete series representations, the Plancherel formula on
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is proved.
仿射对称空间离散序列表示Plancherel定理
affine symmetric spacediscrete seriesPlancherel theorem
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