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This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.

Mathematics. --- Algebraic geometry. --- Associative rings. --- Rings (Algebra). --- Group theory. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Algebraic Geometry. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Algebraic geometry --- Geometry --- Math --- Science --- Geometry, Algebraic. --- Flag manifolds. --- Representations of groups. --- Semisimple Lie groups. --- Schubert varieties. --- MATHEMATICS -- Geometry -- General. --- Geometry, Algebraic --- Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Flag varieties (Mathematics) --- Manifolds, Flag --- Varieties, Flag (Mathematics) --- Algebraic varieties

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This monograph, divided into four parts, presents a comprehensive treatment and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry. Key features: * Accessible to readers from a wide range of fields, with all the necessary background material provided for the nonspecialist * Many new results presented for the first time * Driven by numerous examples * The exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and complex algebraic groups and their representations, as well as other areas of geometry * Comparisons with classical Barlet cycle spaces are given * Good bibliography and index Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work.

Semisimple Lie groups. --- Flag manifolds. --- Twistor theory. --- Automorphic forms. --- Homogeneous spaces. --- Spaces, Homogeneous --- Lie groups --- Automorphic functions --- Forms (Mathematics) --- Twistors --- Congruences (Geometry) --- Field theory (Physics) --- Space and time --- Flag varieties (Mathematics) --- Manifolds, Flag --- Varieties, Flag (Mathematics) --- Algebraic varieties --- Semi-simple Lie groups --- Global differential geometry. --- Topological Groups. --- Differential equations, partial. --- Global analysis. --- Geometry, algebraic. --- Quantum theory. --- Differential Geometry. --- Topological Groups, Lie Groups. --- Several Complex Variables and Analytic Spaces. --- Global Analysis and Analysis on Manifolds. --- Algebraic Geometry. --- Quantum Physics. --- Global analysis (Mathematics) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Algebraic geometry --- Geometry --- Partial differential equations --- Groups, Topological --- Continuous groups --- Geometry, Differential --- Differential geometry. --- Topological groups. --- Lie groups. --- Functions of complex variables. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Algebraic geometry. --- Quantum physics. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Topology --- Complex variables --- Elliptic functions --- Functions of real variables --- Differential geometry

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This book systematically and consistently analyses a wide range of symbols for Europe, critically interpreting their often contradictory or ambiguous dimensions of meaning and uncovering several astonishing aspects of how Europe is currently identified - from above by the political elites as well as from below in critical arts or everyday life; from the inside by European actors but also from the outside by its surrounding others. The focus is on the European Union's main symbols, but they are interpreted in relation to a diverse range of other alternatives, so as to uncover the main facets of

Europe -- Economic integration -- Social aspects. --- Europe -- Symbolic representation. --- Signs and symbols -- Europe. --- Europe --- symbols --- European identity --- European flag --- European anthem --- euro --- European Union --- Group identity --- Signs and symbols --- Representation, Symbolic --- Semeiotics --- Signs --- Symbolic representation --- Symbols --- Abbreviations --- Omens --- Semiotics --- Sign language --- Symbolism --- Visual communication

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Are Tea Party supporters merely a group of conservative citizens concerned about government spending? Or are they racists who refuse to accept Barack Obama as their president because he's not white? Change They Can't Believe In offers an alternative argument-that the Tea Party is driven by the reemergence of a reactionary movement in American politics that is fueled by a fear that America has changed for the worse. Providing a range of original evidence and rich portraits of party sympathizers as well as activists, Christopher Parker and Matt Barreto show that the perception that America is in danger directly informs how Tea Party supporters think and act. In a new afterword, Parker and Barreto reflect on the Tea Party's recent initiatives, including the 2013 government shutdown, and evaluate their prospects for the 2016 election.

Protest movements --- Government, Resistance to --- Political participation --- Tea Party movement. --- Tea Baggers movement --- Teabaggers movement --- Populism --- Citizen participation --- Community action --- Community involvement --- Community participation --- Involvement, Community --- Mass political behavior --- Participation, Citizen --- Participation, Community --- Participation, Political --- Political activity --- Political behavior --- Political rights --- Social participation --- Political activists --- Politics, Practical --- Civil resistance --- Non-resistance to government --- Resistance to government --- Political science --- Political violence --- Insurgency --- Nonviolence --- Revolutions --- Social movements --- History --- Tea Party movement --- Political resistance --- African Americans. --- America. --- American citizenship. --- American flag. --- American identity. --- American politics. --- Asian Americans. --- Barack Obama. --- Catholics. --- Gadsden flag. --- Jews. --- Ku Klux Klan. --- Latinos. --- Obamaphobia. --- Protestants. --- Tea Party. --- U.S. president. --- activism. --- bigotry. --- blacks. --- conservatism. --- conservative principles. --- conservatives. --- equal rights. --- equality. --- evangelicals. --- freedom. --- immigrants. --- intolerance. --- middle-class males. --- minority. --- out-group hostility. --- patriotic imagery. --- patriotism. --- political mobilization. --- public policy. --- racism. --- reactionary conservatives. --- reactionary conservativism. --- reactionary movement. --- right wing. --- social change. --- social movements. --- white males.

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The site at Flag Fen lies at the centre of a once-wet Fenland bay, immediately east of Peterborough. In the Bronze Age a huge alignment of posts crossed a kilometer of wetland to link the two sides of one of the most important and intensively studied prehistoric landscapes in Britain. This volume discusses work carried out at Flag Fen since the completion, in 1995, of the comprehensive Flag Fen Basin Report (EH Archaeology Report, 2001). That monograph published results from the excavations of the Bronze Age platform and the western (Fengate) landfall of the post alignment. Picking up where the last publication left off, this volume looks at the risk to the waterlogged, in-situ prehistoric remains on the site in the context of ongoing de-watering of the Fengate area. In addition it includes detailed investigations of the post alignment's previously unpublished eastern (Northey Island) landfall. New research including oxygen isotope analyses of animal teeth provides interesting, and at times surprising, insights into the economy and the complex role played by domestic animals. The volume also includes a re-assessment of the role that large timbers played at Flag Fen, and elsewhere in Bronze Age Britain.

Bronze age --- Neolithic period --- Water-saturated sites (Archaeology) --- Excavations (Archaeology) --- Archaeological digs --- Archaeological excavations --- Digs (Archaeology) --- Excavation sites (Archaeology) --- Ruins --- Sites, Excavation (Archaeology) --- Archaeology --- Sites, Water-saturated (Archaeology) --- Waterlogged sites (Archaeology) --- Wet sites (Archaeology) --- Wetland archaeology --- Wetland sites (Archaeology) --- Wetlands archaeology --- New Stone age --- Stone age --- Civilization --- Flag Fen Site (England) --- Fens, The (England) --- Fen Country (England) --- Fenland Region (England) --- The Fens (England) --- England --- Antiquities. --- Antiquities