The multiplicity problems for the unitary Ginzburg—Rallis models
The multiplicity problems for the unitary Ginzburg—Rallis models
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DOI：
10.1007/s11856-023-2471-2
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发表时间：
2018-08
影响因子：
1
通讯作者：
C. Wan;Lei Zhang
中科院分区：
文献类型：
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作者：
C. Wan;Lei Zhang
我们考虑了酉群和酉相似群的Ginzburg-Rallis模型的模拟的局部多重性问题。对于酉相似群情形，通过证明模型的局部迹公式，我们证明了所有调和表示的重数公式，这意味着在每个调和局部VoganL-包上重数之和等于1.对于酉群的情况下，我们还证明了一个多重公式的所有回火表示，这意味着在每个回火本地VoganL-包的多重性的总和等于2。
We consider the local multiplicity problems for the analog of the Ginzburg—Rallis model for unitary groups and unitary similitude groups. For the unitary similitude group case, by proving a local trace formula for the model, we prove a multiplicity formula for all tempered representations, which implies that the summation of the multiplicities is equal to 1 over every tempered local VoganL-packet. For the unitary group case, we also prove a multiplicity formula for all tempered representations which implies that the summation of the multiplicities is equal to 2 over every tempered local VoganL-packet.