In representation theory, 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 filtration for Verma modules
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=N(λ), the unique maximal proper submodule of M(λ) The quotients M(λ)i/M(λ)i+1 have non-degenerate contravariant bilinear forms. The Jantzen sum formula holds:
where denotes the formal character.
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