Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Plancherel formula for semisimple Lie groups | Statement: [Iwasawa decomposition, usedIn, Plancherel formula for semisimple Lie groups]

Target entity: Plancherel formula for semisimple Lie groups
Context triple: [Iwasawa decomposition, usedIn, Plancherel formula for semisimple Lie groups]

• A. Plancherel formula for compact Lie groups
  The Plancherel formula for compact Lie groups is a fundamental result in harmonic analysis that decomposes square-integrable functions into irreducible unitary representations, providing an explicit orthogonal expansion and measure on the unitary dual.
• B. Plancherel theorem for real reductive groups chosen
  The Plancherel theorem for real reductive groups is a fundamental result in representation theory that describes how square-integrable functions on a real reductive Lie group decompose into irreducible unitary representations, generalizing Fourier analysis to this non-abelian setting.
• C. Paley–Wiener theorem for real reductive groups
  The Paley–Wiener theorem for real reductive groups is a fundamental result in harmonic analysis that characterizes the image of compactly supported smooth functions under the group Fourier transform in terms of holomorphic functions with specific growth and support conditions.
• D. Proof of the fundamental lemma for Lie algebras
  Proof of the fundamental lemma for Lie algebras is Ngô Bảo Châu’s landmark mathematical work that established a key result in the Langlands program, contributing to his being awarded the Fields Medal.
• E. Plancherel theorem for locally compact abelian groups
  The Plancherel theorem for locally compact abelian groups is a fundamental result in harmonic analysis that identifies the Fourier transform as a unitary isomorphism between an L²-space on the group and an L²-space on its dual group, preserving inner products and norms.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.