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• CommentRowNumber1.
• CommentAuthorDmitri Pavlov
• CommentTimeJun 16th 2019

Added an alternative description of the category of orbits via normalizers.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeApr 8th 2021

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeApr 12th 2021
• (edited Apr 12th 2021)

I am hereby removing the following text from the section “Related concepts”, and instead replaced it by but a pointer to the orbit method.

Whatever parts of this text that is missing at orbit category should be moved to there:

Begin extracted text

### Orbit method

The orbit method is a method in representation theory introduced by Kirillov, Kostant and Souriau; it is a special case of geometric quantization. The orbit method is based on the study of the representations constructed from the coadjoint orbits with Kirillov symplectic structure. The terminology ’geometric quantization’ allows for more general underlying spaces.

Given a compact Lie group $K$ with complexification $G$ and a unitary representation $\rho$ of $K$ on a finite-dimensional complex space $V$, the real orbits of the highest weight vector agrees with the complex orbits, i.e. the orbits of the extension of this representation to the representation of the complexification. These are the coherent state orbits; there is also an infinite-dimensional version for reductive groups and representations which allows them (so-called coherent state representations).

End extracted text

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTime1 day ago

Added the example of a permutation cycle.