Geodesic
Linear Operators Preserving The Real Symplectic Group
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 715-724

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction and s t a t e m e n t of results. Let F be a field and Mn(F) the n X n matrices over F. Set GL(n, F) to be t he units in Mn(F). Suppose H is a subgroup of GL(n, F) and L is an L-linear operator on Mn(F) mapping H into itself. Can L be neatly characterized?Marcus [2] answered this question when F is the complex numbers C and H the unitary group. The set of such L is a group and L has the form L(A) = UAV or L(A) = UA'V where U, V are fixed unitary matrices and A’ is t he transpose of A. 
Pierce, Stephen. Linear Operators Preserving The Real Symplectic Group. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 715-724. doi: 10.4153/CJM-1975-079-7
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