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Search: All articles in the CJM digital archive with keyword Jacquet-Langlands correspondence

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1. CJM 2013 (vol 66 pp. 566)

Choiy, Kwangho
 Transfer of Plancherel Measures for Unitary Supercuspidal Representations between \$p\$-adic Inner Forms Let \$F\$ be a \$p\$-adic field of characteristic \$0\$, and let \$M\$ be an \$F\$-Levi subgroup of a connected reductive \$F\$-split group such that \$\Pi_{i=1}^{r} SL_{n_i} \subseteq M \subseteq \Pi_{i=1}^{r} GL_{n_i}\$ for positive integers \$r\$ and \$n_i\$. We prove that the Plancherel measure for any unitary supercuspidal representation of \$M(F)\$ is identically transferred under the local Jacquet-Langlands type correspondence between \$M\$ and its \$F\$-inner forms, assuming a working hypothesis that Plancherel measures are invariant on a certain set. This work extends the result of MuiÄ and Savin (2000) for Siegel Levi subgroups of the groups \$SO_{4n}\$ and \$Sp_{4n}\$ under the local Jacquet-Langlands correspondence. It can be applied to a simply connected simple \$F\$-group of type \$E_6\$ or \$E_7\$, and a connected reductive \$F\$-group of type \$A_{n}\$, \$B_{n}\$, \$C_n\$ or \$D_n\$. Keywords:Plancherel measure, inner form, local to global global argument, cuspidal automorphic representation, Jacquet-Langlands correspondenceCategories:22E50, 11F70, 22E55, 22E35

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