By Mathieu O., Papadopoulo G.

Allow okay be an algebraically closed box of finite attribute p, and permit be an integer. within the paper, we provide a personality formulation for all uncomplicated rational representations of with optimum weight any a number of of any primary weight. Our formulation is a bit extra common: say dominant weight λ is exact if there are integers such that and . certainly, we compute the nature of any basic module whose maximum weight λ will be written as with every are distinct. by way of stabilization, we get a personality formulation for a relatives of irreducible rational -modules.

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Extra resources for A character formula for a family of simple modular representations of GL(n)

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For supporting evidence, Harris refers to the findings of Peter Laslett and his colleagues on household composition in preindustrial England, as well as to the work of Alan Macfarlane on the development of 'individualism' (Laslett, 1971; Laslett and Wall, 1972; Macfarlane, 1978). He then feels able not only to claim that this feature of the modern family pre-dated the Industrial Revolution by six centuries (Harris, 1983, p. 114), but also to accept the possibility that in England it even existed well before the development of capitalism.

Because the nuclear family, or more precisely the husband, is no longer 'bound to a particular residential location by the occupational, property, or status interests of other [family] members', it is capable of meeting the achievement needs of the now separate economic system (Parsons, 1959, p. 263); hence the relatively high rates of geographical and social mobility in industrial society which further weaken (but do not necessarily destroy) extended kinship relationships. 10 Of particular relevance to the theme of the present discussion is Chris Harris's point about the 'inadequacy of the concept of industrialisation' as the vehicle for explaining the modern family (Harris, 1983, p.

According to Harris, whatever the agrarian family form (or forms) which preceded capitalism, it was superseded by certain distinct family forms associated with transitional 'forms of production' specific to the period between medieval society and 'the rise of industrial society' (ibid, p. 116). That is, In contrast to [the] distinctively agrarian forms of production and family are those characteristics of 'protoindustrialisation', which term has been used to refer to the movement of manufacturing industry into the countryside during the seventeenth and eighteenth centuries.

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