Does anyone know anything about orthogonal and symplectic groups
associated to Gl(n,R)? I am using symplectic/orthogonal in what I think
is the standard sense; I mean, we have an R-module R_M (left- or right- ), and
symplectic /quadratic forms q_S , q_Q respectively . Then the symplectic/orthogonal group
associated with (R_M,Q) is defined to be the subgroup of Gl(n,R) that preserves q_S, resp. q_Q.
I have checked Artin, I Hungerfor(d) Algebra--even Schaum's :) .
Thanks for ideas, refs.