Pierre Bourdieu is perhaps best known in this country for his work on the concept of cultural capital. Work on Bourdieu and class appears on pp 76-77 of book 2 Social Differences and Divisions.
Here is a definition of cultural capital by Mike Savage:
By being based around abstraction, cultural capital bestows upon its possessors the skills and attributes to perform well in the educational process and hence convert their dispositions into educational credentials that will allow them to move into privileged jobs. thus cultural capital allows people to sustain social advantage. It is a separate axis of stratification to economic capital. (Savage. 2002. 'Social Exclusion and Class Analysis' p 77)
On page 78 Savage has extracted the work of Warde studying food consumption in the UK based upon a Bourdieu derived analysis of cultural capital. Warde shows that food consumption has a high degree of consistency over social class and is not just related to income. As Savage points out on p 79 small industrial and commercial employers have similar food tastes to those of thier employees. These differ quite radically from those of the professional classes. You might wish to mae a note of a couple of figures so that you can cite them as examples of the uses of quantitative research in identifying aspects of class.
Savage points out that the concept of cultural capital is different from Weber's notions of status. Status refers to honour / dishonour. Cultural capital involves the inculcation of certain skills and abilities even though they may not be aware of this. Status must be recognised otherwise the status function is lost. Cultural capital on the other hand is frequently at its most effective when it is misrecognised.
For Bourdieu because 'high culture' takes on the position of being universal culture rather than the culture of the ruling elites it thus sustains the power and privileges of the ruling elite. in food consumption for example eating more fresh fruit and vegetables is deemed as being healthier and something that everybody should aspire to as a universal ideal. This approach ignores the class basis of food consumption.
Habitus & Field (See p 81)
Savage also touches upon two other important aspects of Bourdieu's work habitus and field.
Habitus can be described as the internalised, usually unconscious points of view which people hold. These dispositions have the effect of making people feel either uncomfortable or comfortable in different social circumstances. As a result they try and situate themselves within the fields in which they feel most comfortable. Bourdieu notes the idea of pre-reflexive fields and reflexive fields. The latter is less dependent upon money and more upon the ability to function reflexively within powerful institutions which organise the economy and the state. Non-reflexive fields may allow a social actor to accumulate excellent skills such as playing professional football and can earn large amounts of money. But even thebest paid are limited in what they can achieve. They are usually not able to move into other fields and for those not at the top of a sport this can be a problem in later life if sufficient economic capital is not built up.