Jantzen filtration

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In algebra, a Jantzen filtration is a filtration of a Verma module of a semisimple Lie algebra, or a Weyl module of a reductive algebraic group of positive characteristic. Jantzen filtrations were introduced by Jantzen (1979).

Jantzen filtration for Verma modules[edit]

If M(λ) is a Verma module of a semisimple Lie algebra with highest weight λ, then the Janzen filtration is a decreasing filtration

It has the following properties:

  • M(λ)1 is the maximal proper submodule of M(λ)
  • The quotients M(λ)k/M(λ)k+1 have non-degenerate contravariant bilinear forms.
(the Jantzen sum formula)