Comptes Rendus
Algebraic geometry
The full automorphism group of T
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 TG be the closure of a maximal torus TG. 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 GPSL(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 TG la clôture d'un tore maximal TG. Si GPSL(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).

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
     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},
     publisher = {Elsevier},
     volume = {355},
     number = {4},
     year = {2017},
     doi = {10.1016/j.crma.2017.02.008},
     language = {en},
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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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