The group $\mathrm{SL}(n,\mathbb{C})$ .

Question

I am looking for a detailed study of the group $\mathrm{SL}(n,\mathbb{C})$, its topology, subgroups, on any point of view (algebraic, complex or real Lie group theory, etc.). I am interested in any good survey or book able to enlight me on this group !

Answer 1

I don't know the book exactly on $Sl(n,\mathbb{C})$ but you can find some information in different books on Classical groups:

There is a book of Dieudonne Geometry of classical groups, but I am not sure whether it is available in English.

A book of Hermann Weyl The Classical Groups: Their Invariants and Representations discusses representation theory in detail (you can also read any modern book on representations of semisimple groups)

If you are interested in topology note, that topologically $SL(n, \mathbb{C})$ is a product of $SU(n)$ and $\mathbb{R}^{n^2-1}$. So you are intereted in the topology of $SU(n)$ (and that is what you need to search for).

Hope some of these helps.