In algebra, a Jantzen filtration is a filtration of a Verma module

Verma module

Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.The definition of a Verma module looks complicated, but Verma modules are very natural objects, with useful properties...

 of a semisimple Lie algebra, or a Weyl module

Weyl module

In algebra, a Weyl module is a representation of a reductive algebraic group, introduced by and named after Hermann Weyl. In characteristic 0 these representations are irreducible, but in positive characteristic they can be reducible, and their decomposition into irreducible components can be...

 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 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)