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We study representations $G\to H$ where $G$ is either a simple Lie group withreal rank at least 2 or an infinite dimensional orthogonal group of somequadratic form of finite index at least 2 and $H$ is such an orthogonal groupas well. The real, complex and quaternionic cases are considered. Contrarily tothe rank one case, we show that there is no exotic such representations and weclassify these representations.  On the way, we make a detour and prove that the projective orthogonal groups$\mathop{PO}_\mathbf{K}(p,\infty)$ or their orthochronous component (where$\mathbf{K}$ denotes the real, complex or quaternionic numbers) are Polishgroups that are topologically simple but not abstractly simple.

Representations of infinite dimension orthogonal groups of quadratic forms with finite index