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- W1569485632 abstract "In this paper, we study the restriction problem of representations for a non-tempered Arthur packet of $U(3)$. For a pair of tempered $L$-parameters of $(U(n),U(n-1))$, it is known that there is a unique pair of representations in their associateed Vogan $L$-packets which produces the unique Bessel model of these $L$-parameters. We showed that this is ture for some pair of $L$-parameters involving a non-tempered one. On the other hand, we give the precise local theta correspondence for $(U(1),U(3))$ not at the level of $L$-parameters but of individual representations in the framework of the local Langlands correspondence for unitary group. As an applicaiton of these results, we prove an analogue of Ichino-Ikeda conejcture for some non-tempered case. The main tools in this work are the see-saw identity, local theta correspondence for (almost) equal rank cases and recent results on the local Gross-Prasad conjecture on both Fourier-Jacobi and Bessel case." @default.
- W1569485632 created "2016-06-24" @default.
- W1569485632 creator A5022278513 @default.
- W1569485632 date "2015-01-05" @default.
- W1569485632 modified "2023-09-27" @default.
- W1569485632 title "The restriction problem for a non-tempered Arthur packet and local theta correpondence for $(U(1),U(3))$" @default.
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