Comptes Rendus
no. 4
Algebraic geometry
The full automorphism group of T‾
Presented by: 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

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).

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).

Received:
Accepted:
Published online:
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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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

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