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Contents
Contents
Introduction
Chapter 1.
General results from representation theory
1.1.
Basic definitions
1.2.
The Pontryagin dual of a finite abelian group
1.3.
Induced Representations
1.4.
Description of intertwiners
1.5.
A criterion for irreducibility
1.6.
The little groups method
Chapter 2.
Representations constructed by
parabolic induction
2.1.
Conjugacy classes in
GL
2
(
F
q
)
2.2.
Subgroup of upper-triangular matrices
2.3.
Parabolically induced representations for
GL
2
(
F
q
)
2.4.
Conjugacy classes in
SL
2
(
F
q
)
2.5.
Parabolically induced representations for
SL
2
(
F
q
)
Chapter 3.
Construction of the cuspidal representations
3.1.
Projective Representations and Central Extensions
3.2.
The Heisenberg group
3.3.
A special Weil representation
3.4.
The degrees of cuspidal representations
3.5.
Construction of cuspidal representations of
GL
2
(
F
q
)
3.6.
The cuspidal representations of
SL
2
(
F
q
)
Chapter 4.
Some remarks on
GL
n
(
F
q
)
4.1.
Parabolic Induction
4.2.
Cuspidal representations
Appendix A.
Similarity Classes of Matrices
A.1.
Basic properties of matrices
A.2.
Primary decomposition
A.3.
Structure of a primary matrix
A.4.
Block Jordan canonical form
A.5.
Centralisers
A.6.
Perfect fields
Appendix B.
Finite Fields
B.1.
Existence and uniqueness
B.2.
The multiplicative group of
F
q
B.3.
Galois theoretic properties
B.4.
Identification with Pontryagin dual
Bibliography
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