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