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Journal of Lie Theory 25 (2015), No. 4, 903--947
Copyright Heldermann Verlag 2015

Isomorphy Classes of Involutions of SP(2n, k), n>2

Robert W. Benim
Dept. of Mathematics and Computer Science, Pacific University, 2043 College Way, Forest Grove, OR 97116, U.S.A.

Aloysius G. Helminck
Dept. of Mathematics, North Carolina State University, 2108 SAS Hall, Box 8205, Raleigh, NC 27695, U.S.A.

Farrah Jackson Ward
Dept. of Mathematics and Computer Science, Elizabeth City State University, 132 Lane Hall, Campus Box 851, Elizabeth City, NC 27909, U.S.A.

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.

Keywords: Symplectic Group, Involutions, Inner-automophisms.

MSC: 20G15, 20K30

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