is not a base form
1 Form and symmetries
Notice that symmetries form a Lie superalgebra:

 

This superalgebra acts on .
However, it turns out that is not a base form with respect to symmetries.
More precisely:
is invariant but not horizontal
Therefore we cannot integrate over cycles in the base:
does not descend to a PDF on the coset
2 Our solution
We factorize over symmetries, but not over all symmetries.
We will identify a subgroup in the group of symmeties, which has the properties:
It is large enough for the factorspace to have interesting integration cycles.
It is small enough to allow us to define a closed base PDF which we will call .