Given a nilpotent Lie group $G$ (for example the Heisenberg group), what is the most effective method to calculate their unitary representation:
The orbit method due to Kirillov; or
The induction procedure due to Mackey.
Thanks you in advance
2026-04-06 20:58:14.1775509094
Different methods to compute a unitary representation
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I am not sure what the most effective method is, but there are certainly algorithms available for computing unitary irreducible representations of a nilpotent Lie group. For the orbit method there are in particular algorithms to compute polarizing subalgebras (e.g., Vergne polarizing subalgebras) subordinated to a linear functional in the linear dual of the corresponding nilpotent Lie algebra. This is an important step already, and quite challenging in general, from a computational viewpoint. The programs have first been developed by Niels Pederson in REDUCE, and later by Vignon Oussa in MATHEMATICA.