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本書的5篇文章均由2011年6月在北京晨興數學中心舉辦的群表示論研討會的講稿補充或重寫而成，作者都是國際上數論與群表示論方面的著名專家。CorinneBlondel、ColinJ.Bushnell和VincentSécherre的文章從不同的角度由淺入深地闡述了局部群表示理論的最新發展。DavidManderscheid的文章介紹了局部θ對應理論，而FreydoonShahidi的文章則着重論述了Eisenstein級數理論。這些文章都可以作為Langlands綱領的相關領域的入門與深造的重要必讀文獻。
Preface
1Arithmetic of Cuspidal Representations
1.1Cuspidal representations by induction
1.1.1Background and notation
1.1.2Intertwining and Hecke algebras
1.1.3Compact induction
1.1.4An example
1.1.5A broader context
1.2Lattices,orders and strata
1.2.1Lattices and orders
1.2.2Lattice chains
1.2.3Multiplicatives tructures
1.2.4Duality
1.2.5Strata and intertwining
1.2.6Field extensions
1.2.7Minimal elements
1.3Fundamental strata
1.3.1Indamental strata
1.3.2Application to representations
1.3.3The characteristic polynomial
1.3.4Nonsplit fundamental strata
1.4Prime dimension
1.4.1A trivial case
1.4.2The general case
1.4.3The inducing representation
1.4.4Uniqueness
1.4.5Summary
1.5Simple strata and simple characters
1.5.1Adjoint map
1.5.2Critical exponent
1.5.3Construction
1.5.4Intertwining
1.5.5Definitions
1.5.6Interwining
1.5.7Motility
1.6Structure of cuspidal representations
1.6.1Trivial simple characters
1.6.2Occurrence of a simple character
1.6.3Heisenberg representations
1.6.4A further restriction
1.6.5End of the road
1.7Endo-equivalence and lifting
1.7.1Transfer of simple characters
1.7.2Endo-equivalence
1.7.3Invariants
1.7.4Tame lifting
1.7.5Tame induction map for endo-classes
1.8Relation with the Langlands correspondence
1.8.1The Weil group
1.8.2Representations
1.8.3The Langlands correspondence
1.8.4Relation with tame lifting
1.8.5Ramification Theorem
References
……
2Basic Representation Theory of Reductive p-adic Groups
3The Bernstein Decomposition for Smooth Complex Representations of GLn(F)
4Lectures on the Local Theta Correspondence
5An Overview of the Theory of Eisenstein Series
Index
