THE ORBIT STRUCTURE OF THE GELFAND-ZEITLIN GROUP ON n× n MATRICES
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چکیده
In recent work ([9],[10]), Kostant and Wallach construct an action of a simply connected Lie group A ≃ C( n 2 ) on gl(n) using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In [9], the authors show that A-orbits of dimension ( n 2 ) form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe the orbit structure of A on a certain Zariski open subset of regular semisimple elements. In this paper, we describe all A-orbits of dimension ( n 2 ) and thus all polarizations of regular adjoint orbits obtained using Gelfand-Zeitlin theory.
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THE ORBIT STRUCTURE OF THE GELFAND-ZEITLIN GROUP ON n× n MATRICES MARK COLARUSSO AT NOTRE DAME
In recent work ([KW1],[KW2]), Kostant and Wallach construct an action of a simply connected Lie group A ≃ C( n 2 ) on gl(n) using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In [KW1], the authors show that A-orbits of dimension ( n 2 ) form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe ...
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