Algebraic Groups and Discontinuous Subgroups

A. Borel, G. Mostow

Table of contents :
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