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arXiv · 2002.09930

Local normal forms for multiplicity free $U(n)$ actions on coadjoint orbits

Jeremy Lane
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Abstract

Actions of $U(n)$ on $U(n+1)$ coadjoint orbits via embeddings of $U(n)$ into $U(n+1)$ are an important family of examples of multiplicity free spaces. They are related to Gelfand-Zeitlin completely integrable systems and multiplicity free branching rules in representation theory. This paper computes the Hamiltonian local normal forms of all such actions, at arbitrary points, in arbitrary $U(n+1)$ coadjoint orbits. The results are described using combinatorics of interlacing patterns; gadgets that describe the associated Kirwan polytopes.

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Jeremy Lane. 2020-02-23. Local normal forms for multiplicity free $U(n)$ actions on coadjoint orbits. https://doi.org/10.2140/pjm.2020.309.401

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