The characters were unusual and interesting. But I had the sense that the author strived to make them seem mysterious, where the reader may imagine being at the edge of glimpsing into complexities of their motives -- where really, there was not that much to be understood, or at the minimum, the characters conformed certain cultural stereotypes, and were written in such a pre-schemed fashion as to be 'perfectly' explained by Freudian analyses.
For example, the narrator and protagonist, Louisa, was abandoned by her father as a child, and knew that he was a brilliant professor, far away. She thus as a penchant for old men who seem to be brilliant in some way. It also turns out that she feels most pleasure in being completely submissive to an old man, like Gordon, who can treat her like a slave. We can see that the more extreme the abuse and punishment inflicted upon her by Gordon, the more pleasure she feels, due to her registering this abuse as signaling a number of things. First, he is devoted to and trusts her (he refrains from abusing any other women he's been with to this extent). Second, he will not kill her, so this gives her the space to feel extreme pain not only with the full trust that she will be okay, but also as shaped under the context of sex.
It is interesting to think about this second point. We can imagine Louisa's conscious state as uniquely primed towards certain imaginings, given two bottom line facts that she can trust in: her lover Gordon will not kill her, and she feels a lot of pain right now. Perhaps she has felt much pain in her past from her father's abandoning her; she registered this as punishment to her, even though she was just a helpless child. Now, she can be punished by another man, who is old like her father. This is in effect invoking a type of situation that has been central to her past, that has been her core suffering that's shaped her life. But this type of situation is newly now contextualized under sex, which is essentially about her being most wanted and desired by this man. In general, I think some of our most emotionally poignant experiences are those in which old, haunting types of situations, which have been central or salient to us in some way, come up under new contexts, which "solve" or "heal" the reason for suffering of that old type of situation.
But I think we may be invited to such thought by any book on psychoanalytic theory - this novel does not uniquely invite this thought. I wish the characters were more complex, and invited us to think beyond the narratives that are relatively well-established in our culture by the influence of psychoanalytic thought. If one is looking for an absorbing read that could aid in understanding central claims of the psychoanalytic tradition, this would serve that purpose.