Spherical conjugacy classes and the Bruhat decomposition

Carnovale, Giovanna

Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2329-2357.

Soit $G$ un groupe algébrique réductif connexe, sur un corps algébriquement clos de caractéristique zéro ou bonne et impaire. Nous caractérisons les classes de conjugaison sphériques de $G$ comme celles ayant une intersection seulement avec des cellules de Bruhat de $G$ correspondantes à des involutions dans le groupe de Weyl de $G$.

Let $G$ be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in $G$ as those intersecting only Bruhat cells in $G$ corresponding to involutions in the Weyl group of $G$.

Classification : 20GXX, 20E45, 20F55, 14M15
Keywords: Conjugacy class, spherical homogeneous space, Bruhat decomposition
Mot clés : classe de conjugaison, espace homogène sphérique, décomposition de Bruhat

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