Contraction of Hamiltonian K-Spaces

Joachim Hilgert, Christopher Manon, Johan Martens

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popov's horospherical degenerations of complex algebraic varieties with the action of a complex linearly reductive group. We formulate an intrinsic symplectic contraction of a Hamiltonian space, which is a surjective, continuous map on to a new Hamiltonian space that is a symplectomorphism on an explicitly defined dense open subspace. This map is given by a precise formula, using techniques from the theory of symplectic reduction and symplectic implosion. We then show, using the Vinberg monoid, that the gradient-Hamiltonian flow for a horospherical degeneration of an algebraic variety gives rise to this contraction from a general fiber to the special fiber. We apply this construction to branching problems in representation theory, and finally we show how the Gel'fand-Tsetlin integrable system can be understood to arise this way.

Original languageEnglish
Pages (from-to)6255-6309
Number of pages55
JournalInternational Mathematics Research Notices
Issue number20
StatePublished - Oct 1 2017

Bibliographical note

Publisher Copyright:
© The Author(s) 2016. Published by Oxford University Press. All rights reserved.

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Contraction of Hamiltonian K-Spaces'. Together they form a unique fingerprint.

Cite this