I would be glad if someone can give me some (hopefully easy to understand!) references for learning about these groups Osp, USp and PSU and their representations.
I run into these mostly while studying about supersymmetry and I wonder if PSU groups are the same as what are called ``supergroups".
I frequently run into $Osp(3\vert4)$, $USp(2N)$, $PSU(2,2\vert 4)$, $SU(2,2)$ and $SU(2\vert 4)$.
(I don't understand this notation of having a "$\vert$" and I don't know the definition of any of these groups)
Some of the concepts about them that I face are,
The commuting subalgebra of the lie algebra of $SU(2,2,\vert m)$ is that of $SU(2,1\vert m-1)$. The generators of $SU(2,1\vert m-1)$ are related to those of $SU(2,2,\vert m)$ via some "obvious reduction". I don't know what that means.
The "bosonic subgroup" of $SU(2,1\vert m-1)$ is apparently $SU(2,1) \times U(m-1)$. I wonder what this means.
The supersymmetry generators are supposed to transform as "bifundamentals" under the bosonic subalgebra of $SU(2,2)$ and $SU(m)$. (I don't know what is a "bifundamental")
I am very confused about these concepts and would be grateful if someone one help traverse this subject.