局部群表示论.对应和Langlands-Shahidi方法

内容简介

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本书的5篇文章均由2011年6月在北京晨兴数学中心举办的群表示论研讨会的讲稿补充或重写而成，作者都是国际上数论与群表示论方面的著名专家。corinneblondel、colinj.bushnell和vincentsécherre的文章从不同的角度由浅入深地阐述了局部群表示理论的*新发展。davidmanderscheid的文章介绍了局部θ对应理论，而freydoonshahidi的文章则着重论述了eisenstein级数理论。这些文章都可以作为langlands纲领的相关领域的入门与深造的重要必读文献。

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目录

preface1 arithmetic of cuspidal representations colin j.bushnell1.1 cuspidal representations by induction1.1.1 background and notation1.1.2 intertwining and hecke algebras1.1.3 compact induction1.1.4 an example1.1.5 a broader context1.2 lattices, orders and strata1.2.1 lattices and orders1.2.2 lattice chains1.2.3 multiplicative structures1.2.4 duality1.2.5 strata and intertwining1.2.6 field extensions1.2.7 minimal elements1.3 fundamental strata1.3.1 fundamental strata1.3.2 application to representations1.3.3 the characteristic polynomial1.3.4 nonsplit fundamental strata1.4 prime dimension1.4.1 a trivial case1.4.2 the general case1.4.3 the inducing representation1.4.4 uniqueness1.4.5 summary1.5 simple strata and simple characters1.5.1 adjoint map1.5.2 critical exponent1.5.3 construction1.5.4 intertwining1.5.5 definitions1.5.6 interwining1.5.7 motility1.6 structure of cuspidal representations1.6.1 trivial simple characters1.6.2 occurrence of a simple character1.6.3 heisenberg representations1.6.4 a further restriction1.6.5 end of the road1.7 endo-equivalence and lifting1.7.1 transfer of simple characters1.7.2 endo-equivalence1.7.3 invariants1.7.4 tame lifting1.7.5 tame induction map for endo-classes1.8 relation with the langlands correspondence1.8.1 the weil group1.8.2 representations1.8.3 the langlands correspondence1.8.4 relation with tame lifting1.8.5 ramification theoremreferences2 basic representation theory of reductive p-adic groups corinne blondel2.1 smooth representations of locally profinite groups2.1.1 locally profinite groups2.1.2 basic representation theory2.1.3 smooth representations2.1.4 induced representations2.2 admissible representations of locally profinite groups2.2.1 admissible representations2.2.2 haar measure2.2.3 hecke algebra of a locally profinite group2.2.4 coinvariants2.3 schur?s lemma and z-compact representations2.3.1 characters2.3.2 schur?s lemma and central character2.3.3 z-compact representations2.3.4 an example2.4 cuspidal representations of reductive p-adic groups2.4.1 parabolic induction and restriction2.4.2 parabolic pairs2.4.3 cuspidal representations2.4.4 iwahori decomposition2.4.5 smooth irreducible representations are admissiblereferences3 the bernstein decomposition for smooth complex representations of gln(f) vincent s?echerre3.1 compact representations3.1.1 the decomposition theorem3.1.2 formal degree of an irreducible compact representation3.1.3 proof of theorem 1.33.1.4 the compact part of a smooth representation of h3.2 the cuspidal part of a smooth representation3.2.1 from compact to cuspidal representations3.2.2 the group h satisfies the finiteness condition (*)3.2.3 the cuspidal part of a smooth representation3.3 the noncuspidal part of a smooth representation3.3.1 the cuspidal support of an irreducible representation3.3.2 the decomposition theorem3.3.3 further questions3.4 modular smooth representations of gln(f)3.4.1 the l ≠ p case3.4.2 the l ≠ p casereferences4 lecturesonthelocaltheta correspondence david manderscheid4.1 lecture 14.1.1 the heisenberg group4.1.2 the weil representation4.1.3 dependence on ψ4.1.4 now suppose that w1 and w2 are symplectic spaces over f4.1.5 models of ρψ and ωψ4.2 lecture 24.2.1 (reductive) dual pairs4.2.2 theta correspondence4.2.3 an explicit model4.3 lecture 34.3.1 explicit models of the weil representation4.3.2 low dimensional examples4.3.3 general (conjectural) frameworkreferences5 an overview of the theory of eisenstein series freydoon shahidi5.1 intertwining operators5.2 definitions and the statement of the main theorem5.3 constant term5.4 proof of meromorphic continuation for the rank one case5.4.1 preliminaries5.4.2 truncation5.4.3 truncation of et5.4.4 the functional equation for ∧toe5.4.5 proof of meromorphic continutation5.5 proof of the functional equation5.6 convergence of eisenstein series5.7 proof of holomorphy for ν∈ia*referencesindex

封面

书名:局部群表示论.对应和Langlands-Shahidi方法

作者:叶扬波、田野

页数:137

定价:¥45.0

出版社:科学出版社

出版日期:2013-07-01

ISBN:9787030380326

PDF电子书大小:51MB 高清扫描完整版