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.
rbenim@gmail.com
Aloysius G. Helminck
Dept. of Mathematics, North Carolina State University, 2108 SAS Hall, Box 8205, Raleigh, NC 27695, U.S.A.
loek@ncsu.edu
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.
fmjackson@ecsu.edu
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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