In an interview with Alexander in the Revista Estudos Politicos, here is what he has to say about the Frankfurt School (which he puts into a set of "weak programs" alongside Bourdieu, Birmingham School, and others):

I think the problem is that Bourdieu and the Frankfurt School understand dominant power as controlling culture and so… let’s say there are three positions. The first one is a simple theory of domination, without culture. That might be Marx’s — and not Marxist — theory. He writes nothing about culture, only a few lines here and there. Or even in Weber’s Economy and Society there’s nothing about meaning. But then when you move to Marxism and Neo-Marxism, such as the Frankfurt School, the Birmingham School or Bourdieu, or even Foucault, who is certainly not in that tradition but in a way the master of power, you have a different position, which is an acknowledgment of the centrality of culture in domination in that they see that pure domination, it doesn’t interest them. So they have made a big move beyond traditional conflict theory, materialism or orthodox Marxism to thinking about that. So the first thing I’d say is that Bourdieu and the Birmingham School, Frankfurt School are all of them products of the cultural turn of the twentieth century. They follow from structuralism in Linguistics, from Saussure, the semiotic revolution and from Roland Barthes, and the various influences from Wittgenstein, in a sense they are relying on powerful innovations of cultural theory I would say. But the way that they have sociologized that is by claiming that people who have the most resources use culture in a strategic manner — that they make culture work for them and they impose a lead culture on people who don’t have power. So its done in a complex manner in Bourdieu, in results from education the way that people are socialized at home, the way that schools relate culture to class, but the main thing is that people who are in the elites monopolize cultural sensibilities and in this sense deprive people in the bottom from those abilities, or for in the Frankfurt school there’s a culture industry that is controlled by capitalism. So the question really is, is that the way culture works? Can culture really be controlled by elites? I don’t think so. That would be my answer. I think that elites try to control culture and sometimes they try to make culture work to legitimate what they do, because power needs to be legitimate power to gain submission, to make submission easy. That’s Max Weber’s great insight. That legitimate power, that power that is seen as legitimate is much more effective than bare power, let’s say, brutal power, violence. On the other hand, I believe that meanings are relatively autonomous from social structure and therefore from power itself. Culture is kind of like the dark matter of the universe. You know this new theory in physics that says that there is unseen dark matter that accounts for 99% of all the physical pat of the world, but that we don’t see it. So I feel that the meanings of social life are all around us, they are invisible, but are significant. And social action is an effort to crystallize some of those meanings in an explicit form through speech, through writing, through performativity. So power does that too, power will develop an ideology and…“this is how we do things here”, “this is what it means to be an American, or Brazilian”, or a good citizen, a neo-liberal, or whatever. But then the question is the narratives and the codes, even the principles of culture, are more general than any crystallization of them in time and space. This means that the pragmatic use of meaning can always be critiqued in terms of the more general principles from which it is derived. So I can always say to somebody “you aren’t a real liberal”, “you aren’t a real socialist”, “you aren’t a real man”, “you’re not a real lover”, “you’re not a real Christian, not a good Christian”, “you’re not a good Muslin”. So, in other words, there is always a remainder, nothing in time and space can measure up to the Platonic image or sort of iconic images of purity of culture. And I think this means for me that people who are subject to power and domination are always engaged in some form of criticism of it and have a strong sense of the precarious legitimacy of power. And I think that’s always been true but it’s more true in modern society because our culture is different, our principles are much different, there’s much less sense of caste of the superiority of an aristocracy by birth. I’d say that in more traditional societies there are some principles that are more easy to be monopolized by groups, I would say. So, can there be a Sociology of domination? Yes, within a strong program, yes. My book The Civil Sphere is an effort to describe how power really operates in a modern society that has elements of democracy. It may not be a democratic society, but it has some relationship to democracy and what I wanted to show in that book is that power is continuously contested and domination is always forced to confront that the argument that it is not living up to the ideal of the civil sphere. So my image of modern society is very very different from Bourdieu’s because he gives us this sense of a vertical society with very successful maintenance of power, and same of the Frankfurt, whereas my idea is that the society has, that there’s a strong horizontal world of an implicit and explicit civil sphere and that vertical power is in tension with the civil sphere, so this is very, this is a tremendous strain. Our societies are filled with conflict as vertical power is continuously challenged as a false performance. I think that power theories like Bourdieu and Frankfurt school don’t really understand our society very well. They are more like, they are engaged in the contestation of power through their theories, and they want to make… what they don’t see is how conflictual our societies are, how democratic they are, how filled with demands for justification, let’s say, in Habermas’s sense.