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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.02.008/

[1] I. Biswas; S.S. Kannan; D.S. Nagaraj Automorphisms of T‾, C. R. Acad. Sci. Paris, Ser. I, Volume 353 (2015), pp. 785-787

[2] M. Brion; R. Joshua Equivariant Chow ring and Chern classes of wonderful symmetric varieties of minimal rank, Transform. Groups, Volume 13 (2008), pp. 471-493

[3] M. Brion; S. Kumar Frobenius Splitting Methods in Geometry and Representation Theory, Prog. Math., vol. 231, Birkhäuser Boston, Inc., Boston, MA, USA, 2005

[4] D.A. Cox The homogeneous coordinate ring of a toric variety, J. Algebraic Geom., Volume 4 (1995), pp. 17-50

[5] C. De Concini; C. Procesi Complete symmetric varieties, Montecatini, 1982 (Lect. Notes Math.), Volume vol. 996, Springer, Berlin (1983), pp. 1-44

[6] J.E. Humphreys Linear Algebraic Groups, Grad. Texts Math., vol. 21, Springer-Verlag, New York–Heidelberg, 1975

[7] M. Rosenlicht Toroidal algebraic groups, Proc. Amer. Math. Soc., Volume 12 (1961), pp. 984-988

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