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Algebraic groups and Discontinuous Subgroups

About this Title

Armand Borel and George D. Mostow, Editors

Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 1966; Volume 9
ISBNs: 978-0-8218-1409-3 (print); 978-0-8218-3213-4 (online)
DOI: https://doi.org/10.1090/pspum/009

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Table of Contents

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Front/Back Matter

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Algebraic groups, arithmetic groups

• Armand Borel – Linear algebraic groups [MR 0204532]
• Armand Borel – Reduction theory for arithmetic groups [MR 0204533]
• Armand Borel and T. A. Springer – Rationality properties of linear algebraic groups [MR 0205998]
• J. Tits – Classification of algebraic semisimple groups [MR 0224710]
• François Bruhat – $\mathfrak {p}$-adic groups [MR 0213356]
• Nagayoshi Iwahori – Generalized Tits system (Bruhat decompostition) on $p$-adic semisimple groups [MR 0215858]
• Tsuneo Tamagawa – On rational points on projective varieties defined over a complete valuation field [MR 0207701]
• Bertram Kostant – Groups over $Z$ [MR 0207713]
• H. Matsumoto – Subgroups of finite index in certain arithmetic groups [MR 0204534]
• Nelo D. Allan – The problem of the maximality of arithmetic groups [MR 0205997]

Arithmetic properties of algebraic groups. Adèle groups

• Tsuneo Tamagawa – Adèles [MR 0212025]
• Takashi Ono – On Tamagawa numbers [MR 0209290]
• J. G. M. Mars – The Siegel formula for orthogonal groups. I [MR 0209288]
• J. G. M. Mars – The Siegel formula for orthogonal groups. II [MR 0209289]
• R. P. Langlands – The volume of the fundamental domain for some arithmetical subgroups of Chevalley groups [MR 0213362]
• T. A. Springer – Galois cohomology of linear algebraic groups [MR 0210714]
• Martin Kneser – Hasse principle for $H^1$ of simply connected groups [MR 0220736]
• T. A. Springer – Nonabelian $H^2$ in Galois cohomology [MR 0209297]
• Pierre Cartier – Inseparable Galois cohomology [MR 0215863]
• Martin Kneser – Strong approximation [MR 0213361]

Automorphic functions and decomposition of $L^2(G/\Gamma )$

• Armand Borel – Introduction to automorphic forms [MR 0207650]
• R. Godement – The decomposition of $L^2(G/\Gamma )$ for $\Gamma =\mathrm {SL}(2,\,Z)$ [MR 0210827]
• R. Godement – The spectral decomposition of cusp-forms [MR 0210828]
• R. P. Langlands – Eisenstein series [MR 0249539]
• R. P. Langlands – Dimension of spaces of automorphic forms [MR 0212135]
• Ichirô Satake – Spherical functions and Ramanujan conjecture [MR 0211955]
• Yasutaka Ihara – Algebraic curves mod $\mathfrak {p}$ and arithmetic groups [MR 0205992]
• Yasutaka Ihara – Discrete subgroups of $\mathrm {PL}(2, k_{\wp })$ [MR 0205952]

Bounded symmetric domains, holomorphic automorphic forms, moduli

• Walter L. Baily, Jr. – On compactifications of orbit spaces of arithmetic discontinuous groups acting on bounded symmetric domains [MR 0207711]
• Walter L. Baily, Jr. – Fourier-Jacobi series [MR 0219755]
• Jun-ichi Igusa – On the desingularization of Satake compactifications [MR 0217076]
• Walter L. Baily, Jr. – Classical theory of $\theta$-functions [MR 0208016]
• Goro Shimura – Moduli of abelian varieties and number theory [MR 0237507]
• Michio Kuga – Hecke’s polynomial as a generalized congruence Artin $L$-function [MR 0263827]
• Michio Kuga – Fiber varieties over a symmetric space whose fibers are abelian varieties [MR 0206168]
• David Mumford – Families of abelian varieties [MR 0206003]
• Ichirô Satake – Symplectic representations of algebraic groups [MR 0209409]
• William F. Hammond – The modular groups of Hilbert and Siegel [MR 0207653]
• Pierre Cartier – Quantum mechanical commutation relations and theta functions [MR 0216825]

Quotients of symmetric spaces. Deformations

• Shingo Murakami – Cohomologies of vector-valued forms on compact, locally symmetric Riemann manifolds [MR 0206987]
• Howard Garland – On deformations of lattices in Lie groups [MR 0206165]
• Howard Garland – On deformations of discrete groups in the noncompact case [MR 0206166]
• G. D. Mostow – On the conjugacy of subgroups of semisimple groups [MR 0206140]