Howe duality

Target entity: Howe duality
Context triple: [Schur–Weyl duality, generalizedBy, Howe duality]

• A. Schur–Weyl duality
  Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
• B. Alexander duality
  Alexander duality is a theorem in algebraic topology that relates the homology (or cohomology) of a subspace of a sphere to the reduced cohomology of its complement.
• C. Poitou–Tate duality
  Poitou–Tate duality is a fundamental result in Galois cohomology that establishes deep duality relationships between global and local cohomology groups of number fields.
• D. Kazhdan–Lusztig theory
  Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
• E. Poincaré duality
  Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Howe duality
Target entity description: Howe duality is a fundamental principle in representation theory that relates pairs of commuting group actions on a vector space, generalizing the correspondence seen in Schur–Weyl duality.

• A. Schur–Weyl duality
  Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
• B. Alexander duality
  Alexander duality is a theorem in algebraic topology that relates the homology (or cohomology) of a subspace of a sphere to the reduced cohomology of its complement.
• C. Poitou–Tate duality
  Poitou–Tate duality is a fundamental result in Galois cohomology that establishes deep duality relationships between global and local cohomology groups of number fields.
• D. Kazhdan–Lusztig theory
  Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
• E. Poincaré duality
  Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
• F. None of above. chosen