Is anyone aware of any books/papers that discuss the details of the indefinite (special) orthogonal groups $SO(n,m)$, their universal covers, representation theory, etc. (possibly some connections with physics, if any)? My searches thus far have hardly come up with much...
I suppose that I should add that I would be particularly interested in the case where $n,m>1$ (of course there is an enormous litany of references for the case $SO(3,1)$, given its connections to special relativity).
There is some mention of it in a few places that I've come across (e.g. here), I guess I'm just looking for something more focused on these groups themselves (though that's not necessary -- all suggestions are welcome!).
In regards to the potential connections with physics, one is typically interested in the irreducible representations of the universal cover of a given group, and in the standard case of $SO(3,1)$ that would be the double cover $Spin(3,1)$, but $Spin(n,m)$ is not, in general as I understand it, simply connected, so... any help with understanding what it is in more general cases, and its irreps, would be nice. :)
In my opinion, one of the best introductory books for Lie groups is Lie Groups - An introduction trough linear groups by Wulf Rossman.
In that book there are many examples and, I am not wrong, $SO(n,m)$ is explained (at least for some $n$'s and $m=1$).
It is a very good book anyway.