Representation Theory and Automorphic Forms: Instructional Conference, International Centre for Mathematical Sciences, March 1996, Edinburgh, ScotlandT. N. Bailey, Anthony W. Knapp American Mathematical Soc., 1997 - 479 頁 This text is a course in representation theory of semi-simple groups, automorphic forms, and the relations between these two subjects. It is based on the 1996 instructional conference of the International Centre for Mathematical Sciences in Edinburgh. The book begins with an introductory treatment of structure theory and ends with an essay on the current status of functoriality. All papers are intended to provide overviews of the topics they address, and the authors have supplied extensive bibliographies to guide the reader who wants more detail. The aim of the articles is to treat representation theory with two goals in mind: i) to help analysts make systematics use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics, and ii) to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. |
內容
| 1 | |
Characters of Representations and Paths in hsupsubR | 29 |
Irreducible Representations of SL2R | 51 |
General Representation Theory of Real Reductive Lie Groups | 61 |
Infinitesimal Character and Distribution Character of Representations of Reductive Lie Groups | 73 |
Discrete Series | 83 |
The BorelWeil Theorem for Un | 115 |
Induced Representations and the Langlands Classification | 123 |
Introduction to the Langlands Program | 245 |
Representations of GLnF in the Nonarchimedean Case | 303 |
Principal Lfunctions for GLn | 321 |
Functoriality and the Artin Conjecture | 331 |
Theoretical Aspects of the Trace Formula for GL2 | 355 |
An Appendix to the Previous Paper | 407 |
Applications of the Trace Formula | 413 |
Informal Motivation | 433 |
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abelian adeles admissible representation American Mathematical Society analytic Artin Automorphic Forms automorphic representation Borel bundle Cartan subalgebra Cartan subgroup coefficients cohomology compact subgroup complex conjecture conjugacy classes conjugate Corollary corresponding cuspidal representations decomposition defined definition denote differential discrete series representations Eisenstein series element factors finite places finite-dimensional follows functoriality Gal(F/F Galois GL(n GLn(C GLn(F global group G Haar measure Harish-Chandra harmonic analysis hence highest weight Hilbert space holomorphic implies induced representation invariant irreducible representation isomorphism Jacquet K-finite K)-module L-functions Langlands Lemma Let G linear matrix multiplicity nontrivial nonzero number field operator orbital integrals parabolic subgroup Plancherel polynomial positive roots principal series proof properties Proposition quotient reductive group representation of G restriction semisimple Lie groups smooth subgroup of G subset subspace Theorem theory trace formula trivial unitary representation unramified vector Weyl group