Geodesic
Isomorphy Classes of Involutions of SP(2n, k), n>2
Journal of Lie theory, Tome 25 (2015) no. 4, pp. 903-947
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A first characterization of the isomorphism classes of k-involutions for any reductive algebraic groups defined over a perfect field was given by A. G. Helminck [On the Classification of k-involutions I, Adv. in Math. 153 (2000) 1--117] using 3 invariants. In another paper of A. G. Helminck, Ling Wu and C. Dometrius [Involutions of Sl(n, k), (n > 2), Acta Appl. Math. 90 (2006) 91--119] a classification of all involutions on SL(n,k) for k algebraically closed, the real numbers, the p-adic numbers or a finite field was provided. In this paper, we build on these results to develop a detailed characterization of the involutions of SP(2n,k). We use these results to classify the isomorphy classes of involutions of SP(2n, k) where k is any field not of characteristic 2.
Classification : 20G15, 20K30
Mots-clés : Symplectic Group, Involutions, Inner-automophisms 
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     author = {R. W. Benim and A. G. Helminck and F. Jackson Ward},
     title = {Isomorphy {Classes} of {Involutions} of {SP(2n,} k), n>2},
     journal = {Journal of Lie theory},
     pages = {903--947},
     year = {2015},
     volume = {25},
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     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_4_JLT_2015_25_4_a0/}
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R. W. Benim; A. G. Helminck; F. Jackson Ward. Isomorphy Classes of Involutions of SP(2n, k), n>2. Journal of Lie theory, Tome 25 (2015) no. 4, pp. 903-947. http://geodesic.mathdoc.fr/item/JLT_2015_25_4_JLT_2015_25_4_a0/