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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 30th 2019

But I was really looking for a solid reference for the basic statement that the maximal compact subgroup of $O(n,n)$ is $O(n) \times O(n)$.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeMar 30th 2019

There’s a section on maximal compact subgroups of the indefinite orthogonal group here.