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Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107
Author:
ISBN: 0691083509 0691083517 1400881773 9780691083513 9780691083506 Year: 2016 Volume: 107 Publisher: Princeton, NJ : Princeton University Press,

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Abstract

This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups.

Keywords

512 --- Characters of groups --- Finite fields (Algebra) --- Finite groups --- Groups, Finite --- Group theory --- Modules (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Characters, Group --- Group characters --- Groups, Characters of --- Representations of groups --- Rings (Algebra) --- Algebra --- 512 Algebra --- Finite groups. --- Characters of groups. --- Addition. --- Algebra representation. --- Algebraic closure. --- Algebraic group. --- Algebraic variety. --- Algebraically closed field. --- Bijection. --- Borel subgroup. --- Cartan subalgebra. --- Character table. --- Character theory. --- Characteristic function (probability theory). --- Characteristic polynomial. --- Class function (algebra). --- Classical group. --- Coefficient. --- Cohomology with compact support. --- Cohomology. --- Combination. --- Complex number. --- Computation. --- Conjugacy class. --- Connected component (graph theory). --- Coxeter group. --- Cyclic group. --- Cyclotomic polynomial. --- David Kazhdan. --- Dense set. --- Derived category. --- Diagram (category theory). --- Dimension. --- Direct sum. --- Disjoint sets. --- Disjoint union. --- E6 (mathematics). --- Eigenvalues and eigenvectors. --- Endomorphism. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Fiber bundle. --- Finite field. --- Finite group. --- Fourier transform. --- Green's function. --- Group (mathematics). --- Group action. --- Group representation. --- Harish-Chandra. --- Hecke algebra. --- Identity element. --- Integer. --- Irreducible representation. --- Isomorphism class. --- Jordan decomposition. --- Line bundle. --- Linear combination. --- Local system. --- Mathematical induction. --- Maximal torus. --- Module (mathematics). --- Monodromy. --- Morphism. --- Orthonormal basis. --- P-adic number. --- Parametrization. --- Parity (mathematics). --- Partially ordered set. --- Perverse sheaf. --- Pointwise. --- Polynomial. --- Quantity. --- Rational point. --- Reductive group. --- Ree group. --- Schubert variety. --- Scientific notation. --- Semisimple Lie algebra. --- Sheaf (mathematics). --- Simple group. --- Simple module. --- Special case. --- Standard basis. --- Subset. --- Subtraction. --- Summation. --- Surjective function. --- Symmetric group. --- Tensor product. --- Theorem. --- Two-dimensional space. --- Unipotent representation. --- Vector bundle. --- Vector space. --- Verma module. --- Weil conjecture. --- Weyl group. --- Zariski topology.


Book
Rules : a short history of what we live by
Author:
ISBN: 9780691156989 9780691239187 0691156980 0691239185 0691254087 Year: 2022 Publisher: Princeton: Oxford: Princeton University Press,

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Abstract

A panoramic history of rules in the Western worldRules order almost every aspect of our lives. They set our work hours, dictate how we drive and set the table, tell us whether to offer an extended hand or cheek in greeting, and organize the rites of life, from birth through death. We may chafe under the rules we have, and yearn for ones we don't, yet no culture could do without them. In Rules, historian Lorraine Daston traces their development in the Western tradition and shows how rules have evolved from ancient to modern times. Drawing on a rich trove of examples, including legal treatises, cookbooks, military manuals, traffic regulations, and game handbooks, Daston demonstrates that while the content of rules is dazzlingly diverse, the forms that they take are surprisingly few and long-lived.Daston uncovers three enduring kinds of rules: the algorithms that calculate and measure, the laws that govern, and the models that teach. She vividly illustrates how rules can change-how supple rules stiffen, or vice versa, and how once bothersome regulations become everyday norms. Rules have been devised for almost every imaginable activity and range from meticulous regulations to the laws of nature. Daston probes beneath this variety to investigate when rules work and when they don't, and why some philosophical problems about rules are as ancient as philosophy itself while others are as modern as calculating machines.Rules offers a wide-angle view on the history of the constraints that guide us-whether we know it or not.

Keywords

Authority. --- Order (Philosophy) --- Algorithms. --- Law. --- Natural law. --- Order (Philosophy). --- General ethics --- World history --- Authority --- Algorithms --- Law --- Natural law --- Computer algorithms. --- Ethics. --- Actin. --- Algorithm. --- Analogy. --- Aphorism. --- Augustine of Hippo. --- Biotope. --- Braid. --- Brain. --- Brightness. --- Calculation. --- Casuistry. --- Cataclysm (Dragonlance). --- Catechism. --- Chapter 33 (G.I. Bill of Rights). --- Charles Babbage. --- Codification (law). --- Computer program. --- Consonant. --- Culprit. --- Cydnidae. --- Cytoplasmic incompatibility. --- Depiction. --- Designer. --- Dictionary. --- Discretion. --- Drosophila. --- Early Modern literature. --- Electricity. --- Electronics. --- Epithelium. --- Fertilisation. --- Fishing. --- Francis Bacon. --- Gamma ray. --- Genre. --- Good and evil. --- Gottfried Wilhelm Leibniz. --- Government debt. --- Gut flora. --- Hannah Glasse. --- Herder. --- His Family. --- Horntail. --- Household. --- Human intelligence (intelligence gathering). --- Human intelligence. --- Imitation. --- Indication (medicine). --- Insect. --- John Herschel. --- Kinase. --- Lactobacillus. --- Lipid. --- Lookup table. --- Mathematician. --- Mathematics. --- Measurement. --- Metabolism. --- Metabolite. --- Metaphysics. --- Microbiota. --- Microorganism. --- Miguel de Cervantes. --- Monochord. --- Nationalism. --- Natural philosophy. --- Obedience (human behavior). --- Organism. --- Parallel Lives. --- Parchment. --- Pathogen. --- Philosophy. --- Phonetics. --- Polykleitos. --- Precept. --- Prerogative. --- Public utility. --- Publishing. --- Reason. --- Result. --- Rule of Saint Benedict. --- Sect. --- Shavian alphabet. --- Shawl. --- Simon Stevin. --- Spelling rule. --- State of nature. --- Statute. --- Straightedge. --- Subtitle (captioning). --- Subtraction. --- Supplication. --- The Nautical Almanac. --- The Opposite Direction. --- Titer. --- Treatise. --- Tropical rainforest. --- Usage. --- Warfare.

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