1. The Subject Matter. Consider a complex semisimple Lie group G with Lie algebra g and Weyl group W. In this book, we present a geometric perspective on the following circle of ideas: polynomials The "vertices" of this graph are some of the most important objects in representation theory. Each has a theory in its own right, and each has had its own independent historical development. - A nilpotent orbit is an orbit of the adjoint action of G on g which contains the zero element of g in its closure. (For the special linear group 2 G = SL(n,C), whose Lie algebra 9 is all n x n matrices with trace zero, an adjoint orbit consists of all matrices with a given Jordan canonical form; such an orbit is nilpotent if the Jordan form has only zeros on the diagonal. In this case, the nilpotent orbits are classified by partitions of n, given by the sizes of the Jordan blocks.) The closures of the nilpotent orbits are singular in general, and understanding their singularities is an important problem. - The classification of irreducible Weyl group representations is quite old.
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S. A. Lloyd proposes a radically new interpretation of Hobbes's Leviathan that shows transcendent interests--interests that override the fear of death--to be crucial to both Hobbes's analysis of social disorder and his proposed remedy to it. Most previous commentators in the analytic philosophical tradition have argued that Hobbes thought that credible threats of physical force could be sufficient to deter people from political insurrection. Professor Lloyd convincingly shows that because Hobbes took the transcendence of religious and moral interests seriously, he never believed that mere physical force could ensure social order. Lloyd's interpretation demonstrates the ineliminability of that half of Leviathan devoted to religion, and attributes to Hobbes a much more plausible conception of human nature than the narrow psychological egoism traditionally attributed to Hobbes.
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