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Lie groups and their representations occupy an important place in mathematics with applications in such diverse fields as differential geometry, number theory, differential equations and physics. In 1977 a symposium was held in Oxford to introduce this rapidly developing and expanding subject to non-specialists. This volume contains the lectures of ten distinguished mathematicians designed to provide the reader with a deeper understanding of the fundamental theory and appreciate the range of results. This volume contains much to interest mathematicians and theoretical physicists from advanced undergraduate level upwards.
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Lie groups --- Linear algebraic groups --- Congresses --- Groupes algébriques linéaires --- Lie, Algèbres de --- Lie, Groupes de --- Lie groups - Congresses
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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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Category theory. Homological algebra --- Arithmetical algebraic geometry --- Automorphic forms --- Lie groups --- Congresses. --- 51 --- -Automorphic forms --- -Lie groups --- -Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Automorphic functions --- Forms (Mathematics) --- Algebraic geometry, Arithmetical --- Arithmetic algebraic geometry --- Diophantine geometry --- Geometry, Arithmetical algebraic --- Geometry, Diophantine --- Number theory --- Mathematics --- Congresses --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Groups, Lie --- Arithmetical algebraic geometry - Congresses. --- Automorphic forms - Congresses. --- Lie groups - Congresses.
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Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.
Harmonic analysis -- Congresses. --- Harmonic analysis. --- p-adic groups -- Congresses. --- p-adic groups. --- Representations of Lie groups -- Congresses. --- Representations of Lie groups. --- Lie groups --- p-adic groups --- p-adic analysis --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Lie groups. --- Lie algebras. --- Algebras, Lie --- Groups, Lie --- Mathematics. --- Associative rings. --- Rings (Algebra). --- Topological groups. --- Topological Groups, Lie Groups. --- Associative Rings and Algebras. --- Lie algebras --- Symmetric spaces --- Topological groups --- Algebra, Abstract --- Algebras, Linear --- Topological Groups. --- Algebra. --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)
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This volume contains invited articles by top-notch experts who focus on such topics as: modular representations of algebraic groups, representations of quantum groups and crystal bases, representations of affine Lie algebras, representations of affine Hecke algebras, modular or ordinary representations of finite reductive groups, and representations of complex reflection groups and associated Hecke algebras. Representation Theory of Algebraic Groups and Quantum Groups is intended for graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics. Contributors: H. H. Andersen, S. Ariki, C. Bonnafé, J. Chuang, J. Du, M. Finkelberg, Q. Fu, M. Geck, V. Ginzburg, A. Hida, L. Iancu, N. Jacon, T. Lam, G.I. Lehrer, G. Lusztig, H. Miyachi, S. Naito, H. Nakajima, T. Nakashima, D. Sagaki, Y. Saito, M. Shiota, J. Xiao, F. Xu, R. B. Zhang.
Lie groups -- Congresses. --- Quantum groups -- Congresses. --- Representations of groups -- Congresses. --- Lie groups --- Representations of groups --- Quantum groups --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Representations of algebras. --- Quantum groups. --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Mathematics. --- Algebraic geometry. --- Group theory. --- Nonassociative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Number theory. --- Physics. --- Group Theory and Generalizations. --- Algebraic Geometry. --- Topological Groups, Lie Groups. --- Non-associative Rings and Algebras. --- Number Theory. --- Mathematical Methods in Physics. --- Group theory --- Mathematical physics --- Quantum field theory --- Geometry, algebraic. --- Topological Groups. --- Algebra. --- Mathematical physics. --- Groups, Topological --- Continuous groups --- Algebraic geometry --- Geometry --- Physical mathematics --- Physics --- Number study --- Numbers, Theory of --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups
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Acoustics and the Performance of Music connects scientific understandings of acoustics with practical applications to musical performance. Of central importance are the tonal characteristics of musical instruments and the singing voice including detailed representations of directional characteristics. Furthermore, room acoustical concerns related to concert halls and opera houses are considered. Based on this, suggestions are made for musical performance. Included are seating arrangements within the orchestra and adaptations of performance techniques to the performance environment. In the presentation we dispense with complicated mathematical connections and deliberately aim for conceptual explanations accessible to musicians, particularly for conductors. The graphical representations of the directional dependence of sound radiation by musical instruments and the singing voice are unique. Since the first edition was published in 1978, this book has been completely revised and rewritten to include current research. This translation corresponds to the latest (fifth) German edition (2004), which has become a standard reference work for audio engineers and scientists. Acoustics and the Performance of Music addresses issues that are of interest to acousticians, orchestra performers and conductors, audio engineers, architects. Researchers and students of musical acoustics will also find this text valuable.
Acoustical engineering. --- Conducting. --- Harmonic analysis --Congresses. --- Lie algebras --Congresses. --- Lie groups --Congresses. --- Music --Acoustics and physics. --- Music --Performance. --- Theaters --Acoustic properties. --- Music --- Acoustical engineering --- Conducting --- Theaters --- Acoustics & Sound --- Music Philosophy --- Physics --- Music, Dance, Drama & Film --- Physical Sciences & Mathematics --- Acoustics and physics --- Performance --- Acoustic properties --- Acoustics and physics. --- Performance. --- Acoustic properties. --- Opera-houses --- Playhouses (Theaters) --- Theatres --- Acoustic engineering --- Sonic engineering --- Sonics --- Sound engineering --- Sound-waves --- Musical acoustics --- Musical performance --- Performance of music --- Band conducting --- Conducting (Music) --- Music conducting --- Orchestra conducting --- Industrial applications --- Physics. --- Acoustics. --- Engineering Acoustics. --- 517 <061.3> --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517 <061.3> Analysis--?<061.3> --- Analysis--?<061.3> --- Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Engineering --- Arts facilities --- Auditoriums --- Centers for the performing arts --- Music-halls --- Sound --- Monochord --- Harmonic analysis --- Lie algebras --- Lie groups --- Congresses. --- Ergodic theory --- Topological dynamics --- Acoustics in engineering. --- Théorie ergodique --- Théorie ergodique. --- Systèmes dynamiques --- Systèmes dynamiques --- Théorie ergodique --- Analyse harmonique
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