Double Centralizer Properties, Dominant Dimension, and Tilting Modules☆

  title={Double Centralizer Properties, Dominant Dimension, and Tilting Modules☆},
  author={Steffen K{\"o}nig and Inger Heidi Slung{\aa}rd and Changchang Xi},
  journal={Journal of Algebra},
Double centralizer properties play a central role in many parts of algebraic Lie theory. Soergel's double centralizer theorem relates the principal block of the Bernstein–Gelfand–Gelfand category O of a semisimple complex Lie algebra with the coinvariant algebra (i.e., the cohomology algebra of the corresponding flag manifold). Schur–Weyl duality relates the representation theories of general linear and symmetric groups in defining characteristic, or (via the quantized version) in nondefining… 

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