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Number theory --- Discontinuous groups --- Representations of groups --- 51 --- Mathematics --- Discontinuous groups. --- Lie groups. --- Representations of groups. --- 51 Mathematics --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Combinatorial topology --- Functions of complex variables
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Operator theory --- Algebra --- Algèbre --- Bose algebras. --- Representations of groups. --- Mathematical physics --- 51 --- Bose algebras --- Representations of groups --- Hilbert space --- Physical mathematics --- Physics --- Banach spaces --- Hyperspace --- Inner product spaces --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Algebra, Bose --- Algebras, Bose --- Bose algebra --- Operator algebras --- Mathematics --- 51 Mathematics
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Number theory --- L-functions --- Representations of groups --- 517.547.5 --- Automorphic forms --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Automorphic functions --- Forms (Mathematics) --- Functions, L --- -Number theory --- Special classes of analytic functions. Algebraic and algebroid functions. Automorphic functions --- Automorphic forms. --- L-functions. --- Representations of groups. --- 517.547.5 Special classes of analytic functions. Algebraic and algebroid functions. Automorphic functions --- -517.547.5 Special classes of analytic functions. Algebraic and algebroid functions. Automorphic functions
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512 --- Harmonic analysis --- -Representations of groups --- -Semisimple Lie groups --- -Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Algebra --- Congresses --- Semisimple Lie groups --- Representations of Lie groups --- -Algebra --- 512 Algebra --- -512 Algebra --- Semi-simple Lie groups --- Topological groups. Lie groups --- Harmonic analysis. Fourier analysis --- Analyse harmonique (mathématiques) --- Groupes de Lie semi-simples --- Représentations de groupes --- Representations of groups --- Représentations de groupes. --- Harmonic analysis - Congresses --- Semisimple Lie groups - Congresses --- Representations of Lie groups - Congresses
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Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations
Analyse harmonique --- Harmonic analysis --- Harmonische analyse --- Representation des groupes --- Representations of groups --- Vertegenwoordiging van groepen --- Analyse harmonique. --- Représentations de groupes. --- Harmonic analysis. --- Representations of groups. --- Représentations de groupes --- 512.54 --- 517.986.6 --- 51-7 --- 512.81 --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groups. Group theory --- Harmonic analysis of functions of groups and homogeneous spaces --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Lie groups --- 512.81 Lie groups --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- 512.54 Groups. Group theory --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc --- Representation of groups.
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The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity. These representations are realized as some spaces of vanishing cycles of perverse sheaves over configuration spaces. As an application, the bundles of conformal blocks over the moduli spaces of curves are studied. The book is intended for specialists in group representations and algebraic geometry.
Category theory. Homological algebra --- Quantum groups --- Representations of groups --- Sheaf theory --- Mathematical physics --- Mathematical Theory --- Applied Physics --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Bundeltheorie --- Cohomology [Sheaf ] --- Faisceaux [Théorie des ] --- Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Groupes des quantiques --- Mathematische fysica --- Physical mathematics --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Physique mathématique --- Physique théorique --- Quanta [Groupes des ] --- Quantumgroepen --- Representation des groupes --- Sheaf cohomology --- Sheaves (Algebraic topology) --- Sheaves [Theory of ] --- Théorie des faisceaux --- Vertegenwoordiging van groepen --- Wiskundige fysica --- Algebraic geometry. --- Differential geometry. --- Topology. --- Nonassociative rings. --- Rings (Algebra). --- Algebraic topology. --- Quantum physics. --- Algebraic Geometry. --- Differential Geometry. --- Non-associative Rings and Algebras. --- Algebraic Topology. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Topology --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Differential geometry --- Algebraic geometry --- Quantum groups. --- Representations of groups. --- Sheaf theory. --- Cohomology, Sheaf --- Sheaves, Theory of --- Algebraic topology --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Quantum field theory
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A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.
511.33 --- Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- 511.33 Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- Automorfe vormen --- Automorphic forms --- Formes automorphes --- Representation des groupes --- Representations of groups --- Trace formulas --- Vertegenwoordiging van groepen --- Formulas, Trace --- Discontinuous groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Automorphic functions --- Forms (Mathematics) --- Analytical and multiplicative number theory. Asymptotics. Sieves etc --- Representations of groups. --- Trace formulas. --- Automorphic forms. --- 0E. --- Addition. --- Admissible representation. --- Algebraic group. --- Algebraic number field. --- Approximation. --- Archimedean property. --- Automorphic form. --- Automorphism. --- Base change. --- Big O notation. --- Binomial coefficient. --- Canonical map. --- Cartan subalgebra. --- Cartan subgroup. --- Central simple algebra. --- Characteristic polynomial. --- Closure (mathematics). --- Combination. --- Computation. --- Conjecture. --- Conjugacy class. --- Connected component (graph theory). --- Continuous function. --- Contradiction. --- Corollary. --- Counting. --- Coxeter element. --- Cusp form. --- Cyclic permutation. --- Dense set. --- Density theorem. --- Determinant. --- Diagram (category theory). --- Discrete series representation. --- Discrete spectrum. --- Division algebra. --- Eigenvalues and eigenvectors. --- Eisenstein series. --- Exact sequence. --- Existential quantification. --- Field extension. --- Finite group. --- Finite set. --- Fourier transform. --- Functor. --- Fundamental lemma (Langlands program). --- Galois extension. --- Galois group. --- Global field. --- Grothendieck group. --- Group representation. --- Haar measure. --- Harmonic analysis. --- Hecke algebra. --- Hilbert's Theorem 90. --- Identity component. --- Induced representation. --- Infinite product. --- Infinitesimal character. --- Invariant measure. --- Irreducibility (mathematics). --- Irreducible representation. --- L-function. --- Langlands classification. --- Laurent series. --- Lie algebra. --- Lie group. --- Linear algebraic group. --- Local field. --- Mathematical induction. --- Maximal compact subgroup. --- Multiplicative group. --- Nilpotent group. --- Orbital integral. --- P-adic number. --- Paley–Wiener theorem. --- Parameter. --- Parametrization. --- Permutation. --- Poisson summation formula. --- Real number. --- Reciprocal lattice. --- Reductive group. --- Root of unity. --- Scientific notation. --- Semidirect product. --- Special case. --- Spherical harmonics. --- Subgroup. --- Subset. --- Summation. --- Support (mathematics). --- Tensor product. --- Theorem. --- Trace formula. --- Unitary representation. --- Weil group. --- Weyl group. --- Zero of a function.
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"This volume in the ASD series (VIII, 1) publishes texts by Erasmus related to the Fathers of the Church. Erasmus himself considered these among his major contributions to Christianity and the Church. He edited many Fathers and wrote Vitae of three theologians: John Chrysostom, Origen and - his most important one - Jerome. He provides portraits of the theologians and his views on them, but also a kind of self-portrait. He even forged a text himself: 'Cyprian's De duplici martyrio'. His many editions of the Church Fathers and other theologians contain prefaces which provide us with information about the theologians, and with remarks on Erasmus' views on them. Thus, we get a clearer understanding of Erasmus and his theology." -- Information provided by publisher
Humanities. --- History. --- Regional and national history. --- European history. --- Erasmus, Desiderius, --- Erasmus Roterodamus, Desiderius --- Erasmus --- Erasmus, Desiderius --- Érasme --- Desiderius Erasmus --- Erasm, Dezideriĭ --- Erasme, Désiré --- Erasmo, --- Erasmo, Desidério --- Erasmus, --- Ėrazm, --- Erazm, --- Roterodamus, Erasmus --- Rotterdamskiĭ, Ėrazm --- Rotterdamský, Erasmus Desiderius --- Роттердамский, Эразм --- Эразм, --- Ерасм, Дезидерий --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- 223.5 --- Prediker. Qohelet (Ecclesiastes) --- Bible. --- Ba-yon Tipan --- Bagong Tipan --- Jaji ma Hungi --- Kainē Diathēkē --- New Testament --- Nouveau Testament --- Novo Testamento --- Novum Testamentum --- Novyĭ Zavet --- Novyĭ Zavi︠e︡t Gospoda nashego Īisusa Khrista --- Novyĭ Zavit --- Nuevo Testamento --- Nuovo Testamento --- Nye Testamente --- Perjanjian Baru --- Dhamma sacʻ kyamʻʺ --- Injīl --- Criticism, interpretation, etc. --- History --- Fathers of the church --- Church fathers --- Patristics --- Philosophy, Patristic --- Christians --- Cyprian, --- 873.4 ERASMUS ROTERODAMUS, DESIDERIUS <01> --- 873.4 ERASMUS ROTERODAMUS, DESIDERIUS <01> Humanistisch Latijnse literatuur--Bibliografieën. Catalogi--ERASMUS ROTERODAMUS, DESIDERIUS --- Humanistisch Latijnse literatuur--Bibliografieën. Catalogi--ERASMUS ROTERODAMUS, DESIDERIUS --- 873.4 ERASMUS ROTERODAMUS, DESIDERIUS --- 873.4 ERASMUS ROTERODAMUS, DESIDERIUS Humanistisch Latijnse literatuur--ERASMUS ROTERODAMUS, DESIDERIUS --- Humanistisch Latijnse literatuur--ERASMUS ROTERODAMUS, DESIDERIUS --- 873.4 ERASMUS ROTERODAMUS, DESIDERIUS:2 --- Humanistisch Latijnse literatuur-:-Godsdienst. Theologie--ERASMUS ROTERODAMUS, DESIDERIUS --- エラスムス, デシデリウス --- Christian literature, Latin (Medieval and modern). --- Latin literature, Medieval and modern. --- 1500-1599. --- Theology - Early works to 1800 --- Philosophy --- Classical languages --- Pronunciation. --- López de Zúñiga, Diego, --- Translating --- Christian life --- Confession --- Cousturier, Pierre, --- Bible --- Valla, Lorenzo --- Plutarque --- Luther, Martin --- Philosophy and religion - Early works to 1800. --- Christian literature, Latin (Medieval and modern) --- Latin literature, Medieval and modern --- Latin Christian literature, Medieval and modern --- Jean (Book of the New Testament) --- Johanisi (Book of the New Testament) --- Johannesevangelium --- John (Book of the New Testament) --- Yohan pogŭm --- Yohane den (Book of the New Testament) --- Yūḥannā (Book of the New Testament) --- Ioganaĭ (Book of the New Testament) --- Иоганай (Book of the New Testament) --- Desiderius Erasmus, --- Erasm, Dezideriĭ, --- Erasme, Désiré, --- Erasmo, Desidério, --- Roterodamus, Erasmus, --- Rotterdamskiĭ, Ėrazm, --- Rotterdamský, Erasmus Desiderius, --- Роттердамский, Эразм, --- Ерасм, Дезидерий, --- אראסמוס, דסידריוס, --- Theology --- Philosophy and religion --- Fathers of the church. --- Humanismus. --- Kirchenväter. --- Pères de l'Église. --- Rezeption.
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