The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.
The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.
Nicolas Poussin, perhaps the most famous French painter of the seventeenth century, lived and worked for many years in Rome. Yet he remained deeply engaged with cultural and political transformations occurring in France, argues Todd R Olson in this original exploration of Poussin's paintings, their production, and their reception. Poussin's references to ancient literature and sculpture addressed a political elite -- the Robe nobility -- whose humanist education in classical antiquity equipped them to relate Greek and Roman history to contemporary events and to deploy ancient precedents in legalistic and political arguments. When the French civil war known as the Fronde erupted in the middle of the seventeenth century, the paintings that Poussin exported to France responded directly in both subject and style to the crisis in monarchical authority and the disenfranchisement of his Robe patrons. Olson demonstrates that Poussin's association with a disgraced political group, his loss of official support, and his exile in Italy imbued his history paintings with a symbolic weight. The painter's audience considered the hardearned pleasures of his restrained, difficult pictorial style a benchmark of integrity as well as a criticism of the Regency's indiscriminate collecting practices and taste for foreign luxury. Poussin transformed the easel painting -- its making and collection -- into an expression of cultural and political commitments binding a community. Olson's fresh insights reveal the importance of this painter's work to a learned and powerful French constituency at a critical moment in French history and demonstrate that Poussin's famously timeless style was far more responsive tohistorical contingencies than has been previously recognized.
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