The asymptotic behavior of invariant collective motion

Knop F (1994)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1994


Publisher: Springer Verlag (Germany)

Book Volume: 116

Pages Range: 309-328

Journal Issue: 1-3

DOI: 10.1007/BF01231563


Let G be reductive and X a smooth G-variety. Then the cotangent bundle T_X^* carries a symplectic structure and the G-action gives rise to a moment map T_X^*-->g^* (with g=Lie G). Let f be a regular function on T_X^* which is induced by an Ad G-invariant function on g^*. The associated Hamiltonian flow is called invariant collective. In this paper we prove that the invariant collective flow is symmetric under the little Weyl group W_X of X.

The main application is: Let Z(X) be the set of all G-invariant valuations of k(X) which are trivial on k(X)^B, B=Borel subgroup. Then Z(X) is canonically in bijection to a Weyl chamber of W_X.

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How to cite


Knop, F. (1994). The asymptotic behavior of invariant collective motion. Inventiones Mathematicae, 116(1-3), 309-328.


Knop, Friedrich. "The asymptotic behavior of invariant collective motion." Inventiones Mathematicae 116.1-3 (1994): 309-328.

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