
D.15.12 orbitparam_lib
 Library:
 orbitparam.lib
 Purpose:
 Parametrizing orbits of unipotent actions
 Authors:
 J. Boehm, boehm at mathematik.unikl.de
S. Papadakis, papadak at math.ist.utl.pt
 Overview:
 This library implements the theorem of ChevalleyRosenlicht as stated in Theorem 3.1.4 of [Corwin, Greenleaf].
Given a set of strictly upper triangular n x n matrices L_1,...,L_c which generate
a Lie algebra as a vector space, and a vector v of size n, the
function
parametrizeOrbit constructs a parametrization of the orbit of v under
the action of exp(<L_1,...,L_c>).
To compute exp of the Lie algebra elements corresponding
to the parameters we require that the characteristic of the base field is zero or larger than n.
By determining the parameters from bottom to top
this allows you to find an element in the orbit with (at least) as many zeros as the dimension of the
orbit.
Note: Theorem 3.1.4 of [Corwin, Greenleaf] uses strictly lower triangular matrices.
 References:
 Laurence Corwin, Frederick P. Greenleaf: Representations of Nilpotent Lie Groups and their Applications: Volume 1, Part 1, Basic Theory and Examples, Cambridge University Press (2004).
Procedures:
