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 compact Lie groups | Statement: [Weyl denominator, roleIn, Plancherel formula for compact Lie groups]

Target entity: Plancherel formula for compact Lie groups
Context triple: [Weyl denominator, roleIn, Plancherel formula for compact Lie groups]

• A. Plancherel theorem for real reductive groups
  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.
• B. 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.
• 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. Plancherel measure
  The Plancherel measure is a canonical measure on the unitary dual of a group that describes how the regular representation decomposes into irreducible unitary representations in harmonic analysis.
• E. Harish-Chandra character formula
  The Harish-Chandra character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible admissible representations of real reductive Lie groups.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Plancherel formula for compact Lie groups
Target entity description: 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.

• A. Plancherel theorem for real reductive groups
  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.
• B. 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.
• 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. Plancherel measure
  The Plancherel measure is a canonical measure on the unitary dual of a group that describes how the regular representation decomposes into irreducible unitary representations in harmonic analysis.
• E. Harish-Chandra character formula
  The Harish-Chandra character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible admissible representations of real reductive Lie groups.
• F. None of above. chosen