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In this classic work, Anthony W. Knapp offers a survey of representation theory of semisimple Lie groups in a way that reflects the spirit of the subject and corresponds to the natural learning process. This book is a model of exposition and an invaluable resource for both graduate students and researchers. Although theorems are always stated precisely, many illustrative examples or classes of examples are given. To support this unique approach, the author includes for the reader a useful 300-item bibliography and an extensive section of notes.

Semisimple Lie groups. --- Representations of groups. --- Groupes de Lie semi-simples --- Représentations de groupes --- Semisimple Lie groups --- Representations of groups --- Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Représentations de groupes --- 512.547 --- 512.547 Linear representations of abstract groups. Group characters --- Linear representations of abstract groups. Group characters --- Abelian group. --- Admissible representation. --- Algebra homomorphism. --- Analytic function. --- Analytic proof. --- Associative algebra. --- Asymptotic expansion. --- Automorphic form. --- Automorphism. --- Bounded operator. --- Bounded set (topological vector space). --- Cartan subalgebra. --- Cartan subgroup. --- Category theory. --- Characterization (mathematics). --- Classification theorem. --- Cohomology. --- Complex conjugate representation. --- Complexification (Lie group). --- Complexification. --- Conjugate transpose. --- Continuous function (set theory). --- Degenerate bilinear form. --- Diagram (category theory). --- Dimension (vector space). --- Dirac operator. --- Discrete series representation. --- Distribution (mathematics). --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Existence theorem. --- Explicit formulae (L-function). --- Fourier inversion theorem. --- General linear group. --- Group homomorphism. --- Haar measure. --- Heine–Borel theorem. --- Hermitian matrix. --- Hilbert space. --- Holomorphic function. --- Hyperbolic function. --- Identity (mathematics). --- Induced representation. --- Infinitesimal character. --- Integration by parts. --- Invariant subspace. --- Invertible matrix. --- Irreducible representation. --- Jacobian matrix and determinant. --- K-finite. --- Levi decomposition. --- Lie algebra. --- Locally integrable function. --- Mathematical induction. --- Matrix coefficient. --- Matrix group. --- Maximal compact subgroup. --- Meromorphic function. --- Metric space. --- Nilpotent Lie algebra. --- Norm (mathematics). --- Parity (mathematics). --- Plancherel theorem. --- Projection (linear algebra). --- Quantifier (logic). --- Reductive group. --- Representation of a Lie group. --- Representation theory. --- Schwartz space. --- Semisimple Lie algebra. --- Set (mathematics). --- Sign (mathematics). --- Solvable Lie algebra. --- Special case. --- Special linear group. --- Special unitary group. --- Subgroup. --- Summation. --- Support (mathematics). --- Symmetric algebra. --- Symmetrization. --- Symplectic group. --- Tensor algebra. --- Tensor product. --- Theorem. --- Topological group. --- Topological space. --- Topological vector space. --- Unitary group. --- Unitary matrix. --- Unitary representation. --- Universal enveloping algebra. --- Variable (mathematics). --- Vector bundle. --- Weight (representation theory). --- Weyl character formula. --- Weyl group. --- Weyl's theorem. --- ZPP (complexity). --- Zorn's lemma.