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This book is based on a graduate course taught at the University of Paris. The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne-Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.

Lie groups. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups

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Group theory --- Finite groups --- Modules (Algebra) --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Rings (Algebra) --- Groups, Finite --- Groupes finis --- Représentations de groupes --- Modules (algèbre) --- Integral representations --- représentations intégrales --- Représentations de groupes. --- représentations intégrales.

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These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.

Trees (Graph theory) --- Graph theory --- Automorphisms. --- Harmonic analysis. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Symmetry (Mathematics) --- Automorphisms --- Harmonic analysis --- Representations of groups --- Arbres (Théorie des graphes) --- Analyse harmonique --- Représentations de groupes