#### Vol. 309, No. 2, 2020

 Recent Issues Vol. 311: 1 Vol. 310: 1  2 Vol. 309: 1  2 Vol. 308: 1  2 Vol. 307: 1  2 Vol. 306: 1  2 Vol. 305: 1  2 Vol. 304: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
Local normal forms for multiplicity free $U(n)$ actions on coadjoint orbits

### Jeremy Lane

Vol. 309 (2020), No. 2, 401–419
##### Abstract

Actions of $U\left(n\right)$ on $U\left(n+1\right)$ coadjoint orbits via embeddings of $U\left(n\right)$ into $U\left(n+1\right)$ 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 $U\left(n+1\right)$ coadjoint orbits. The results are described using combinatorics of interlacing patterns; gadgets that describe the associated Kirwan polytopes.

##### Keywords
coadjoint orbits, multiplicity free spaces, local normal form, Gelfand–Zeitlin, integrable systems
##### Mathematical Subject Classification 2010
Primary: 53D20
Secondary: 14M27, 37J35