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Linear Operators Preserving The Real Symplectic Group

Published online by Cambridge University Press:  20 November 2018

Stephen Pierce
Stephen Pierce*
Affiliation:
University of Toronto, Toronto, Ontario
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 715 - 724
Copyright
Copyright © Canadian Mathematical Society 1975

References

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