Let be a connected reductive algebraic group. We prove that for a quasi-affine -spherical variety the weight monoid is determined by the weights of its non-trivial -actions that are homogeneous with respect to a Borel subgroup of . As an application we get that a smooth affine spherical variety that is non-isomorphic to a torus is determined by its automorphism group (considered as an ind-group) inside the category of smooth affine irreducible varieties.
Soit un groupe réductif connexe. Nous montrons que le monoïde des poids d’une variété -sphérique quasi-affine est déterminé par les poids de ses -actions non triviales homogènes sous l’action d’un sous-groupe de Borel de . Comme application, nous obtenons qu’une variété sphérique affine lisse non isomorphe à un tore est déterminée par son groupe des automorphismes (considéré comme un ind-groupe) dans la catégorie des variétés irréductibles affines lisses.
Accepted:
Published online:
DOI: 10.5802/jep.149
Keywords: Automorphism groups of quasi-affine varieties, quasi-affine spherical varieties, root subgroups, quasi-affine toric varieties
Mot clés : Groupes des automorphismes des variétés quasi-affines, variétés sphériques quasi-affines, sous-groupes de racines, variétés toriques quasi-affines
Andriy Regeta 1; Immanuel van Santen 2
@article{JEP_2021__8__379_0, author = {Andriy Regeta and Immanuel van Santen}, title = {Characterizing smooth affine spherical varieties via the automorphism group}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {379--414}, publisher = {\'Ecole polytechnique}, volume = {8}, year = {2021}, doi = {10.5802/jep.149}, mrnumber = {4218162}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.149/} }
TY - JOUR AU - Andriy Regeta AU - Immanuel van Santen TI - Characterizing smooth affine spherical varieties via the automorphism group JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 379 EP - 414 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.149/ DO - 10.5802/jep.149 LA - en ID - JEP_2021__8__379_0 ER -
%0 Journal Article %A Andriy Regeta %A Immanuel van Santen %T Characterizing smooth affine spherical varieties via the automorphism group %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 379-414 %V 8 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.149/ %R 10.5802/jep.149 %G en %F JEP_2021__8__379_0
Andriy Regeta; Immanuel van Santen. Characterizing smooth affine spherical varieties via the automorphism group. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 379-414. doi : 10.5802/jep.149. https://jep.centre-mersenne.org/articles/10.5802/jep.149/
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