Proof of the Knop conjecture
[Preuve de la conjecture de Knop]
Losev, Ivan V.1
1 Massachusetts Institute of Technology Department of Mathematics Room 2-101 77 Massachusetts Avenue Cambridge MA 02139 (USA)
Annales de l'Institut Fourier, Tome 59 (2009) no. 3, pp. 1105-1134.

Dans cet article nous prouvons la conjecture de Knop qui affirme que deux variétés affines sphériques lisses avec le même monoïde des poids sont isomorphes de manière équivariante. On énonce et prouve également une propriété d’unicité pour des variétés affines sphériques non nécessairement lisses.

In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoid are equivariantly isomorphic. We also state and prove a uniqueness property for (not necessarily smooth) affine spherical varieties.

DOI : 10.5802/aif.2459
Classification : 14R20, 53D20
Keywords: Spherical varieties, weight monoids, systems of spherical roots, multiplicity free Hamiltonian actions
Mot clés : variété sphérique, monoïde
Losev, Ivan V. 1

1 Massachusetts Institute of Technology Department of Mathematics Room 2-101 77 Massachusetts Avenue Cambridge MA 02139 (USA) 
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Losev, Ivan V. Proof of the Knop conjecture. Annales de l'Institut Fourier, Tome 59 (2009) no. 3, pp. 1105-1134. doi : 10.5802/aif.2459. https://www.numdam.org/articles/10.5802/aif.2459/

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