Proof of the fundamental lemma for Lie algebras

Target entity: Proof of the fundamental lemma for Lie algebras
Context triple: [Ngo Bao Chau, notableWork, Proof of the fundamental lemma for Lie algebras]

• A. 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.
• B. 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.
• C. Beilinson–Bernstein localization theorem
  The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
• D. Real Reductive Groups II
  Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
• E. Deligne–Lusztig theory
  Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Proof of the fundamental lemma for Lie algebras
Target entity description: 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.

• A. 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.
• B. 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.
• C. Beilinson–Bernstein localization theorem
  The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
• D. Real Reductive Groups II
  Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
• E. Deligne–Lusztig theory
  Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
• F. None of above. chosen