Bott–Samelson theorem

Target entity: Bott–Samelson theorem
Context triple: [Raoul Bott, knownFor, Bott–Samelson theorem]

• A. 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.
• B. 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.
• C. Borel–Weil theorem
  The Borel–Weil theorem is a fundamental result in representation theory that realizes irreducible representations of compact Lie groups as spaces of holomorphic sections of line bundles over their flag manifolds.
• D. Bernstein–Gelfand–Gelfand resolution
  The Bernstein–Gelfand–Gelfand resolution is a fundamental construction in representation theory that provides an explicit, exact sequence resolving finite-dimensional representations of semisimple Lie algebras using complexes of Verma modules.
• 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: Bott–Samelson theorem
Target entity description: The Bott–Samelson theorem is a fundamental result in algebraic topology and geometry that provides a resolution of singularities for Schubert varieties via Bott–Samelson varieties, illuminating the topology and cohomology of flag manifolds.

• A. 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.
• B. 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.
• C. Borel–Weil theorem
  The Borel–Weil theorem is a fundamental result in representation theory that realizes irreducible representations of compact Lie groups as spaces of holomorphic sections of line bundles over their flag manifolds.
• D. Bernstein–Gelfand–Gelfand resolution
  The Bernstein–Gelfand–Gelfand resolution is a fundamental construction in representation theory that provides an explicit, exact sequence resolving finite-dimensional representations of semisimple Lie algebras using complexes of Verma modules.
• 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