Contraction of Hamiltonian K-spaces

Joachim Hilgert, Christopher Manon, Johan Martens

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 onto 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 pages42
JournalInternational Mathematics Research Notices
Volume2017
Issue number20
Early online date20 Sept 2016
DOIs
Publication statusPublished - 1 Oct 2017

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