Abstract
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 language | English |
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Pages (from-to) | 6255-6309 |
Number of pages | 55 |
Journal | International Mathematics Research Notices |
Volume | 2017 |
Issue number | 20 |
DOIs | |
State | Published - 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