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Abstract
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Actions of
on
coadjoint orbits
via embeddings of
into
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
coadjoint orbits. The results are described using combinatorics of interlacing
patterns; gadgets that describe the associated Kirwan polytopes.
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Keywords
coadjoint orbits, multiplicity free spaces, local normal
form, Gelfand–Zeitlin, integrable systems
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Mathematical Subject Classification 2010
Primary: 53D20
Secondary: 14M27, 37J35
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Milestones
Received: 21 February 2020
Revised: 1 October 2020
Accepted: 8 October 2020
Published: 14 January 2021
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