Methods of Representation Theory

Target entity: Methods of Representation Theory
Context triple: [Israel Gelfand, notableWork, Methods of Representation Theory]

• A. The Classical Groups: Their Invariants and Representations
  The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
• B. 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.
• C. 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.
• D. Harish-Chandra isomorphism
  The Harish-Chandra isomorphism is a fundamental result in representation theory that identifies the center of the universal enveloping algebra of a semisimple Lie algebra with the algebra of Weyl group–invariant polynomials on a Cartan subalgebra.
• 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: Methods of Representation Theory
Target entity description: Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.

• A. The Classical Groups: Their Invariants and Representations
  The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
• B. 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.
• C. 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.
• D. Harish-Chandra isomorphism
  The Harish-Chandra isomorphism is a fundamental result in representation theory that identifies the center of the universal enveloping algebra of a semisimple Lie algebra with the algebra of Weyl group–invariant polynomials on a Cartan subalgebra.
• 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