Preface
1 Arithmetic of Cuspidal Representations Colin J.Bushnell
1.1 Cuspidal representations by induction
1.1.1 Background and notation
1.1.2 Intertwining and Hecke algebras
1.1.3 Compact induction
1.1.4 An example
1.1.5 A broader context
1.2 Lattices, orders and strata
1.2.1 Lattices and orders
1.2.2 Lattice chains
1.2.3 Multiplicative structures
1.2.4 Duality
1.2.5 Strata and intertwining
1.2.6 Field extensions
1.2.7 Minimal elements
1.3 Fundamental strata
1.3.1 Fundamental strata
1.3.2 Application to representations
1.3.3 The characteristic polynomial
1.3.4 Nonsplit fundamental strata
1.4 Prime dimension
1.4.1 A trivial case
1.4.2 The general case
1.4.3 The inducing representation
1.4.4 Uniqueness
1.4.5 Summary
1.5 Simple strata and simple characters
1.5.1 Adjoint map
1.5.2 Critical exponent
1.5.3 Construction
1.5.4 Intertwining
1.5.5 Definitions
1.5.6 Interwining
1.5.7 Motility
1.6 Structure of cuspidal representations
1.6.1 Trivial simple characters
1.6.2 Occurrence of a simple character
1.6.3 Heisenberg representations
1.6.4 A further restriction
1.6.5 End of the road
1.7 Endo-equivalence and lifting
1.7.1 Transfer of simple characters
1.7.2 Endo-equivalence
1.7.3 Invariants
1.7.4 Tame lifting
1.7.5 Tame induction map for endo-classes
1.8 Relation with the Langlands correspondence
1.8.1 The Weil group
1.8.2 Representations
1.8.3 The Langlands correspondence
1.8.4 Relation with tame lifting
1.8.5 Ramification Theorem
References
2 Basic Representation Theory of Reductive p-adic Groups Corinne Blondel
2.1 Smooth representations of locally profinite groups
2.1.1 Locally profinite groups
2.1.2 Basic representation theory
2.1.3 Smooth representations
2.1.4 Induced representations
2.2 Admissible representations of locally profinite groups
2.2.1 Admissible representations
2.2.2 Haar measure
2.2.3 Hecke algebra of a locally profinite group
2.2.4 Coinvariants
2.3 Schur?s Lemma and Z-compact representations
2.3.1 Characters
2.3.2 Schur?s Lemma and central character
2.3.3 Z-compact representations
2.3.4 An example
2.4 Cuspidal representations of reductive p-adic groups
2.4.1 Parabolic induction and restriction
2.4.2 Parabolic pairs
2.4.3 Cuspidal representations
2.4.4 Iwahori decomposition
2.4.5 Smooth irreducible representations are admissible
References
3 The Bernstein Decomposition for Smooth Complex Representations of GLnF Vincent S?echerre
3.1 Compact representations
3.1.1 The decomposition theorem
3.1.2 Formal degree of an irreducible compact representation
3.1.3 Proof of Theorem 1.3
3.1.4 The compact part of a smooth representation of H
3.2 The cuspidal part of a smooth representation
3.2.1 From compact to cuspidal representations
3.2.2 The group H satisfies the finiteness condition *
3.2.3 The cuspidal part of a smooth representation
3.3 The noncuspidal part of a smooth representation
3.3.1 The cuspidal support of an irreducible representation
3.3.2 The decomposition theorem
3.3.3 Further questions
3.4 Modular smooth representations of GLnF
3.4.1 The l ≠ p case
3.4.2 The l ≠ p case
References
4 LecturesontheLocalTheta Correspondence David Manderscheid
4.1 Lecture 1
4.1.1 The Heisenberg group
4.1.2 The Weil representation
4.1.3 Dependence on ψ
4.1.4 Now suppose that W1 and W2 are symplectic spaces over F
4.1.5 Models of ρψ and ωψ
4.2 Lecture 2
4.2.1 Reductive dual pairs
4.2.2 Theta correspondence
4.2.3 An explicit model
4.3 Lecture 3
4.3.1 Explicit models of the Weil representation
4.3.2 Low dimensional examples
4.3.3 General conjectural framework
References
5 An Overview of the Theory of Eisenstein Series Freydoon Shahidi
5.1 Intertwining operators
5.2 Definitions and the statement of the main theorem
5.3 Constant term
5.4 Proof of meromorphic continuation for the rank one case
5.4.1 Preliminaries
5.4.2 Truncation
5.4.3 Truncation of ET
5.4.4 The functional equation for ∧ToE
5.4.5 Proof of meromorphic continutation
5.5 Proof of the functional equation
5.6 Convergence of Eisenstein series
5.7 Proof of holomorphy for ν∈ia*
References
Index
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