Reductive group actions on affine varieties and their doubling

Panyushev, Dmitri I.

doi:10.5802/aif.1479

Panyushev, Dmitri I.

Annales de l'Institut Fourier, Volume 45 (1995) no. 4, p. 929-950

Abstract
Résumé

We study $G$ -actions of the form $(G : X \times X^{*})$ , where $X^{*}$ is the dual (to $X$ ) $G$ -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action $(G : X)$ is given. It is shown that the doubled actions have a number of nice properties, if $X$ is spherical or of complexity one.

Nous étudions les actions de la forme $(G : X \times X^{*})$ où $X^{*}$ est la $G$ -variété duale de $X$ . Ces actions sont appelées les doubles. Nous donnons une interprétation géométrique de la complexité de l’action $(G : X)$ . Nous montrons que les actions doublées ont un certain nombre de bonnes propriétés, lorsque $X$ est sphérique ou de complexité un.

MR 96i:14039 | Zbl 0831.14022 | 1 citation in Numdam

DOI : https://doi.org/10.5802/aif.1479

@article{AIF_1995__45_4_929_0,
     author = {Panyushev, Dmitri I.},
     title = {Reductive group actions on affine varieties and their doubling},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {45},
     number = {4},
     year = {1995},
     pages = {929-950},
     doi = {10.5802/aif.1479},
     zbl = {0831.14022},
     mrnumber = {96i:14039},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1995__45_4_929_0}
}

Panyushev, Dmitri I. Reductive group actions on affine varieties and their doubling. Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 929-950. doi : 10.5802/aif.1479. http://www.numdam.org/item/AIF_1995__45_4_929_0/

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