Transfer of Plancherel Measures for Unitary Supercuspidal Representations between p-adic Inner Forms

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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 Πᵢ₌₁ʳ SLₙᵢ M Πᵢ₌₁ʳ GLₙᵢ for positive integers r and nᵢ. 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 Muić and Savin (2000) for Siegel Levi subgroups of the groups SO₄ₙ and Sp₄ₙ under the local Jacquet-Langlands correspondence. It can be applied to a simply connected simple F-group of type E₆ or E₇, and a connected reductive F-group of type Aₙ, Bₙ, Cₙ or Dₙ.