Comptes Rendus
no. 4
Algebraic geometry
The full automorphism group of T‾
[Le groupe complet des automorphismes de T‾]

Présenté par : Claire Voisin

Indranil Biswas1 ; Subramaniam Senthamarai Kannan2 ; Donihakalu Shankar Nagaraj3
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India
3 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 452-454.

Soit G‾ la compactification magnifique d'un groupe algébrique affine simple G de type adjoint défini sur C. Soit T‾⊂G‾ la clôture d'un tore maximal T⊂G. Si G≠PSL(2,C), nous montrons que le groupe de tous les automorphismes de la variété T‾ est le produit semi-direct NG(T)⋊D, où NG(T) est le normalisateur de T dans G et D est le groupe de tous les automorphismes du diagramme de Dynkin. Remarquez que si G=PSL(2,C), alors T‾=CP1 et donc dans ce cas Aut(T‾)=PSL(2,C).

Let G‾ be the wonderful compactification of a simple affine algebraic group G of adjoint type defined over C. Let T‾⊂G‾ be the closure of a maximal torus T⊂G. We prove that the group of all automorphisms of the variety T‾ is the semi-direct product NG(T)⋊D, where NG(T) is the normalizer of T in G and D is the group of all automorphisms of the Dynkin diagram, if G≠PSL(2,C). Note that if G=PSL(2,C), then T‾=CP1 and so in this case Aut(T‾)=PSL(2,C).

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DOI : 10.1016/j.crma.2017.02.008
Indranil Biswas 1 ; Subramaniam Senthamarai Kannan 2 ; Donihakalu Shankar Nagaraj 3

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India
3 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India 
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     author = {Indranil Biswas and Subramaniam Senthamarai Kannan and Donihakalu Shankar Nagaraj},
     title = {The full automorphism group of $ \stackrel{‾}{T}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {452--454},
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Indranil Biswas; Subramaniam Senthamarai Kannan; Donihakalu Shankar Nagaraj. The full automorphism group of $ \stackrel{‾}{T}$. Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 452-454. doi : 10.1016/j.crma.2017.02.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.02.008/

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