Character Analysis
Aussie Louis is a bit of outsider in this odd group of six. He's the son of an Australian banker and jeepers does he reference that fact a lot; "My father is a banker in Brisbane" is The Waves version of "One time at band camp…"
Louis spends a lot of time working through an apparently intense feeling of inferiority; he's constantly afraid that people will make fun of his accent or his father's profession… and eventually his own. For example, in an early scene in the nursery school, Louis proclaims (internally, we assume, since he doesn't get booted out of class for suddenly yelling out),
I will not conjugate the verb... until Bernard has said it. My father is a banker in Brisbane and I speak with an Australian accent. I will wait and copy Bernard. He is English. They are all English. (1b.55)
Louis's hyper class-consciousness (not the radical kind) and inferiority complex may be responsible for his decision to avoid a scholarly career, even though we later learn that he is an awesomely intelligent and gifted student.
It is important to note that Louis may have been based in part on T. S. Eliot, a fellow poet who was great friends with Woolf and was actually a banker himself… though not in Brisbane.
Anger Management
Perhaps because of his feelings of inferiority, Louis seems a bit on the angry side. He constantly mentions that he can hear a "great beast" that is "stamping" nearby (1b.6), creating an image of pent-up violence that might mirror Louis's own sense of being trapped and wronged. Presumably Brisbane banker Daddy has something to do with this.
Heart Authority
Louis is a stickler for authority; he's the only one of the three central male narrators that can stand Dr. Crane, their headmaster at school, who is a buttoned-up authority figure. Again, perhaps because of his inferiority issues, Louis seems extra interested in people who demonstrate strength and autonomy. Daddy issues, much?
Down Under on the Down Low
As already noted (and noted so often in The Waves) Louis's father is a "banker from Brisbane." This fact causes Louis a considerable amount of angst; he is extremely self-conscious about his Aussie accent and the fact that his father is a tradesman. He fears that his schoolmates will judge him on the basis of these national and class differences.
Later on in his life, Louis has an affair with Rhoda, who has also felt like an outsider for her entire life (and therefore probably understands him a bit better than the average bear). We never get to see much hot Rhoda-Louis action though.
At the same time that he's feeling this crippling inferiority complex, in the grand tradition of overcompensating, Louis asserts his superiority to the others, noting, "I know more than they will ever know" (1b.55). In fact, he suggests that he possesses first-hand knowledge of an impossible range of eras and cultures within human history, with repeated references to watching men and women walking along the ancient Nile. We're going to call you on that right here and now, Louis. You did not know Cleopatra.
Despite Louis's sense that he doesn't quite belong, people like Bernard and Neville clearly admire him. Bernard, in particular, is jealous of Louis's great aptitude with languages, and he is galled by the fact that Louis does not pursue a career as an artist or scholar (instead of working at a shipping company).
That's not to say that Louis gives up his love of language and poetry entirely as an adult, of course. He remains fascinated by both—and their capacity to capture human experience—throughout the book.
And that's not the only way in which Louis leads a double-life. Even after he becomes a respected businessman, he maintains an attraction to the seamier side of London and its inhabitants:
...I still keep my attic room. There I open the usual little book; there I watch the rain glisten on the tiles till they shine like a policeman's waterproof; there I see the broken windows in poor people's houses; the lean cats; some slattern squinting in a cracked looking-glass as she arranges her face for the street corner; there Rhoda sometimes comes. For we are lovers. (6b.6)
We hope someone tells Louis that peeping in people's windows like that is creeptastic.
Like the others, he is preoccupied by the nature of his connection to others, frequently expressing a desire to bring people together using The Power of Words. He and Bernard are on the same page in that respect, it seems.
Louis's Timeline