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1 Straightforward descent does not work
2 Modified PDF

Descent to double coset

The form does not descend from to ; but we will prove that for some subgroups , it can be modified in a natural way, so that the modified form does descend to

    1 Straightforward descent does not work

    2 Modified PDF

1 Straightforward descent does not work

We are identifying with the double coset . Let be a special canonical transformation, i.e. . It follows immediately that is invariant under the left shift . But is not horizonthal; for we have:

Therefore:

does not descend from to

2 Modified PDF

However, we identify a class of subalgebras for which we can construct the base form . Being a base form, it descends to , where is the Lie group generated by the flows of elements of .