گروه‌های جبری و زیرگروه‌های ناپیوسته: سمپوزیوم گروه‌های جبری، ۵ تا ۶ اوت ۱۹۶۵، بولدر، کلرادو

Endmatter......Page 0 Title......Page 1 Copyright......Page 2 Foreword......Page 3 Contents......Page 4 I. Algebraic Groups, Arithmetic Groups......Page 7 Linear Algebraic Groups by A. Borel......Page 8 Reduction Theory for Arithmetic Groups by A. Borel......Page 25 Rationality Properties of Linear Algebraic Groups by A. Borel and T. A. Springer......Page 31 Classification of Algebraic Semisimple Groups by J. Tits......Page 38 $\mathfrak {p}$-adic Groups by F. Bruhat......Page 68 Generalized Tits System (Bruhat Decomposition)....by N. Iwahori......Page 76 On Rational Points on Projective Varieties....by T. Tamagawa......Page 89 Groups over $Z$ by B. Kostant......Page 95 Subgroups of Finite Index in Certain Arithmetic Groups by H. Matsumoto......Page 104 The Problem of the Maximality of Arithmetic Groups by N. D. Allan......Page 109 II. Arithmetic Properties of Algebraic Groups. Adele Groups......Page 115 Adeles by T. Tamagawa......Page 116 On Tamagawa Numbers by T. Ono......Page 125 The Siegel Formula for Orthogonal Groups. I by J.G.M. Mars......Page 136 The Siegel Formula for Orthogonal Groups. II by J.G.M. Mars......Page 141 The Volume of the Fundamental Domain....by R.P. Langlands......Page 146 Galois Cohomology of Linear Algebraic Groups by T.A. Springer......Page 152 Hasse Principle for $H^1$ of Simply Connected Groups by M. Kneser......Page 162 Nonabelian $H^2$ in Galois Cohomology by T. A. Springer......Page 167 Inseparable Galois Cohomology by P. Cartier......Page 186 Strong Approximation by M. Kneser......Page 190 III. Automorphic Functions and Decomposition of $L^2(G/\Gamma)$......Page 200 Introduction to Automorphic Forms by A. Borel......Page 201 The Decomposition of $L^2(G/\Gamma)$ for $\Gamma =SL(2, Z)$ by R. Godement......Page 213 The Spectral Decomposition of Cusp-Forms by R. Godement......Page 227 Eisenstein Series by R.P. Langlands......Page 237 Dimension of Spaces of Automorphic Forms by R.P. Langlands......Page 255 Spherical Functions and Ramanujan Conjecture by I. Satake......Page 260 Algebraic Curves Mod $\mathfrak {p}$ and Arithmetic Groups by Y. Ihara......Page 267 Discrete Subgroups of $PL(2, k_{\wp}$ by Y. Ihara......Page 274 IV. Bounded Symmetric Domains, Holomorphic Automorphic Forms, Moduli......Page 281 On Compactifications of Orbit Spaces.... by W.L. Baily, Jr.......Page 282 Fourier-Jacobi Series by W.L. Baily, Jr.......Page 297 On the Desingularization of Satake Compactifications by J.-i. Igusa......Page 302 Classical Theory of $\theta$-functions by W.L. Baily, Jr.......Page 307 Moduli of Abelian Varieties and Number Theory by G. Shimura......Page 313 Hecke's Polynomial as a Generalized Congruence Artin L-function by M. Kuga......Page 334 Fiber Varieties over a Symmetric Space.... by M. Kuga......Page 339 Families of Abelian Varieties by D. Mumford......Page 348 Symplectic Representations of Algebraic Groups by I. Satake......Page 353 The Modular Groups of Hilbert and Siegel by W.F. Hammond......Page 359 Quantum Mechanical Commutation Relations.... by P. Cartier......Page 362 V. Quotients of Symmetric Spaces. Deformations......Page 385 Cohomologies of Vector-valued Forms on....by S. Murakami......Page 386 On Deformations of Lattices in Lie Groups by H. Garland......Page 399 On Deformations of Discrete Groups in the Noncompact Case by H. Garland......Page 404 On the Conjugacy of Subgroups of Semisimple Groups by G.D. Mostow......Page 412 Index......Page 419 Authors......Page 423 pspum9-frnt.pdf -1 Frontmatter 1 Title 1 Copyright 2 Foreword 3 Contents 4 pspum9-ptI.pdf 1 I. Algebraic Groups, Arithmetic Groups 7 Linear Algebraic Groups by A. Borel 8 Reduction Theory for Arithmetic Groups by A. Borel 25 Rationality Properties of Linear Algebraic Groups by A. Borel and T. A. Springer 31 Classification of Algebraic Semisimple Groups by J. Tits 38 $\mathfrak {p}$-adic Groups by F. Bruhat 68 Generalized Tits System (Bruhat Decomposition)....by N. Iwahori 76 On Rational Points on Projective Varieties....by T. Tamagawa 89 Groups over $Z$ by B. Kostant 95 Subgroups of Finite Index in Certain Arithmetic Groups by H. Matsumoto 104 The Problem of the Maximality of Arithmetic Groups by N. D. Allan 109 pspum9-ptII.pdf 1 II. Arithmetic Properties of Algebraic Groups. Adele Groups 115 Adeles by T. Tamagawa 116 On Tamagawa Numbers by T. Ono 125 The Siegel Formula for Orthogonal Groups. I by J.G.M. Mars 136 The Siegel Formula for Orthogonal Groups. II by J.G.M. Mars 141 The Volume of the Fundamental Domain....by R.P. Langlands 146 Galois Cohomology of Linear Algebraic Groups by T.A. Springer 152 Hasse Principle for $H^1$ of Simply Connected Groups by M. Kneser 162 Nonabelian $H^2$ in Galois Cohomology by T. A. Springer 167 Inseparable Galois Cohomology by P. Cartier 186 Strong Approximation by M. Kneser 190 pspum9-ptIII.pdf 1 III. Automorphic Functions and Decomposition of $L^2(G/\Gamma)$ 200 Introduction to Automorphic Forms by A. Borel 201 The Decomposition of $L^2(G/\Gamma)$ for $\Gamma =SL(2, Z)$ by R. Godement 213 The Spectral Decomposition of Cusp-Forms by R. Godement 227 Eisenstein Series by R.P. Langlands 237 Dimension of Spaces of Automorphic Forms by R.P. Langlands 255 Spherical Functions and Ramanujan Conjecture by I. Satake 260 Algebraic Curves Mod $\mathfrak {p}$ and Arithmetic Groups by Y. Ihara 267 Discrete Subgroups of $PL(2, k_{\wp}$ by Y. Ihara 274 pspum9-ptIV.pdf 1 IV. Bounded Symmetric Domains, Holomorphic Automorphic Forms, Moduli 281 On Compactifications of Orbit Spaces.... by W.L. Baily, Jr. 282 Fourier-Jacobi Series by W.L. Baily, Jr. 297 On the Desingularization of Satake Compactifications by J.-i. Igusa 302 Classical Theory of $\theta$-functions by W.L. Baily, Jr. 307 Moduli of Abelian Varieties and Number Theory by G. Shimura 313 Hecke's Polynomial as a Generalized Congruence Artin L-function by M. Kuga 334 Fiber Varieties over a Symmetric Space.... by M. Kuga 339 Families of Abelian Varieties by D. Mumford 348 Symplectic Representations of Algebraic Groups by I. Satake 353 The Modular Groups of Hilbert and Siegel by W.F. Hammond 359 Quantum Mechanical Commutation Relations.... by P. Cartier 362 pspum9-ptV.pdf 1 V. Quotients of Symmetric Spaces. Deformations 385 Cohomologies of Vector-valued Forms on....by S. Murakami 386 On Deformations of Lattices in Lie Groups by H. Garland 399 On Deformations of Discrete Groups in the Noncompact Case by H. Garland 404 On the Conjugacy of Subgroups of Semisimple Groups by G.D. Mostow 412 pspum9-bck.pdf 1 Endmatter -1 Index 419 Authors 423