Dynamical Weyl group

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Plan:

  • -----simple Lie algebra
  • -----------weight
    • c -------dominant weight
    • -----has singular vector
    • and ---- generic
  • --------Verma module
  • -------------finite-dimensional module
    • -weight,
    • -weight subspace
  • -------------dominant weight
  • ----------finite-dimensional module
  • ----space of g-invariant homomorphismata
  • ----space of g-invariant homomorphisma

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  • For generic,
  • For generic,
  • For sufficiently large, is an isomorphism.
  • -----------dynamical Weyl operator
  • ----commutes with