I agree with Simon but if I may suggest the problem with representation using a post- modern philosophical framework is one of language.In other words the uniqueness of the subject is lost in the introduction of said subject to a symbolic language. While I give this argument merit I think you will find your answer in the writings of Foucault. I would suggest the Archaeology of Knowledge (1972) and Power and Knowledge (1977). Foucault does not fully answer the representation problem as you put it but his work goes a long way to solve this problem.
Secondly the issue of postmodernism raises for social researchers is one or denying a simple binary as previous "critical research" had done. Postmodernism argues for complexity and power dynamics or relationships in a much more interaction between objects on the subject thus the subject become invisible hence the problem with representation.
Last, I suggest a look into discourse analysis as a possible avenue toward introducing the problem of representation and a critical discourse analysis as an approach to overcoming the problem at hand.
You might find Nancy Fraser's Rethinking Recognition helpful as it integrates representational politics with economic activism. And I think responds well to the postmodern paralysis issue:
the dichotomous categorization of Essentialism vs Anti- Essentialism can lucidly expound this issue. Plato and Aristotle believed that objects, events and concepts have an essential reality behind them , that is, have a representation as form with identifiable characteristics. Every object or reality can be operationally defined and its building blocks tangibly specified.
Anti-essentialism or non-esssentialism ,conversely, points out that here are no specific representations or tangible unified features for any even object or entity. Realities are constructed and reconstructed differently by different viewers much like a postmodern approach.