Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings. These topics are intertwined, representing a common meeting of algebra, geometry, and analysis.

Group theory --- Complex analysis --- Number theory --- RIEMANN SURFACES --- Discontinuous groups --- congresses --- Congresses --- Riemann surfaces --- Congresses. --- Groupes discontinus --- Combinatorial topology --- Functions of complex variables --- Surfaces, Riemann --- Functions --- Abelian variety. --- Adjunction (field theory). --- Affine space. --- Algebraic curve. --- Algebraic structure. --- Analytic function. --- Arithmetic genus. --- Automorphism. --- Bernhard Riemann. --- Boundary (topology). --- Cauchy sequence. --- Cauchy–Schwarz inequality. --- Cayley–Hamilton theorem. --- Closed geodesic. --- Combination. --- Commutative diagram. --- Commutator subgroup. --- Compact Riemann surface. --- Complex dimension. --- Complex manifold. --- Complex multiplication. --- Complex space. --- Complex torus. --- Congruence subgroup. --- Conjugacy class. --- Convex set. --- Cyclic group. --- Degeneracy (mathematics). --- Diagram (category theory). --- Diffeomorphism. --- Differential form. --- Dimension (vector space). --- Disjoint sets. --- E7 (mathematics). --- Endomorphism. --- Equation. --- Equivalence class. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Finite group. --- Finitely generated group. --- Fuchsian group. --- Fundamental domain. --- Fundamental lemma (Langlands program). --- Fundamental polygon. --- Galois extension. --- Holomorphic function. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Hurwitz's theorem (number theory). --- Inclusion map. --- Inequality (mathematics). --- Inner automorphism. --- Intersection (set theory). --- Irreducibility (mathematics). --- Isomorphism class. --- Isomorphism theorem. --- Jacobian variety. --- Jordan curve theorem. --- Kleinian group. --- Limit point. --- Mapping class group. --- Metric space. --- Monodromy. --- Monomorphism. --- Möbius transformation. --- Non-Euclidean geometry. --- Orthogonal trajectory. --- Permutation. --- Polynomial. --- Power series. --- Projective variety. --- Quadratic differential. --- Quadric. --- Quasi-projective variety. --- Quasiconformal mapping. --- Quotient space (topology). --- Rectangle. --- Riemann mapping theorem. --- Riemann surface. --- Schwarzian derivative. --- Simply connected space. --- Simultaneous equations. --- Special case. --- Subgroup. --- Subsequence. --- Surjective function. --- Symmetric space. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological space. --- Topology. --- Uniqueness theorem. --- Unit disk. --- Variable (mathematics). --- Winding number. --- Word problem (mathematics). --- RIEMANN SURFACES - congresses --- Discontinuous groups - Congresses --- Geometrie algebrique --- Fonctions d'une variable complexe --- Surfaces de riemann

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions.Originally published in 1960.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

515.16 --- 515.16 Topology of manifolds --- Topology of manifolds --- Riemann surfaces. --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Surfaces, Riemann --- Functions --- Analytic function. --- Axiom of choice. --- Basis (linear algebra). --- Betti number. --- Big O notation. --- Bijection. --- Bilinear form. --- Bolzano–Weierstrass theorem. --- Boundary (topology). --- Boundary value problem. --- Bounded set (topological vector space). --- Branch point. --- Canonical basis. --- Cauchy sequence. --- Cauchy's integral formula. --- Characterization (mathematics). --- Coefficient. --- Commutator subgroup. --- Compact space. --- Compactification (mathematics). --- Conformal map. --- Connected space. --- Connectedness. --- Continuous function (set theory). --- Continuous function. --- Coset. --- Cross-cap. --- Dirichlet integral. --- Disjoint union. --- Elementary function. --- Elliptic surface. --- Exact differential. --- Existence theorem. --- Existential quantification. --- Extremal length. --- Family of sets. --- Finite intersection property. --- Finitely generated abelian group. --- Free group. --- Function (mathematics). --- Fundamental group. --- Green's function. --- Harmonic differential. --- Harmonic function. --- Harmonic measure. --- Heine–Borel theorem. --- Homeomorphism. --- Homology (mathematics). --- Ideal point. --- Infimum and supremum. --- Isolated point. --- Isolated singularity. --- Jordan curve theorem. --- Lebesgue integration. --- Limit point. --- Line segment. --- Linear independence. --- Linear map. --- Maximal set. --- Maximum principle. --- Meromorphic function. --- Metric space. --- Normal operator. --- Normal subgroup. --- Open set. --- Orientability. --- Orthogonal complement. --- Partition of unity. --- Point at infinity. --- Polyhedron. --- Positive harmonic function. --- Principal value. --- Projection (linear algebra). --- Projection (mathematics). --- Removable singularity. --- Riemann mapping theorem. --- Riemann surface. --- Semi-continuity. --- Sign (mathematics). --- Simplicial homology. --- Simply connected space. --- Singular homology. --- Skew-symmetric matrix. --- Special case. --- Subgroup. --- Subset. --- Summation. --- Support (mathematics). --- Taylor series. --- Theorem. --- Topological space. --- Triangle inequality. --- Uniform continuity. --- Uniformization theorem. --- Unit disk. --- Upper and lower bounds. --- Upper half-plane. --- Weyl's lemma (Laplace equation). --- Zorn's lemma.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The theory of D-modules deals with the algebraic aspects of differential equations. These are particularly interesting on homogeneous manifolds, since the infinitesimal action of a Lie algebra consists of differential operators. Hence, it is possible to attach geometric invariants, like the support and the characteristic variety, to representations of Lie groups. By considering D-modules on flag varieties, one obtains a simple classification of all irreducible admissible representations of reductive Lie groups. On the other hand, it is natural to study the representations realized by functions on pseudo-Riemannian symmetric spaces, i.e., spherical representations. The problem is then to describe the spherical representations among all irreducible ones, and to compute their multiplicities. This is the goal of this work, achieved fairly completely at least for the discrete series representations of reductive symmetric spaces. The book provides a general introduction to the theory of D-modules on flag varieties, and it describes spherical D-modules in terms of a cohomological formula. Using microlocalization of representations, the author derives a criterion for irreducibility. The relation between multiplicities and singularities is also discussed at length.Originally published in 1990.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Differentiable manifolds. --- D-modules. --- Representations of groups. --- Lie groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Modules (Algebra) --- Differential manifolds --- Manifolds (Mathematics) --- Affine space. --- Algebraic cycle. --- Algebraic element. --- Analytic function. --- Annihilator (ring theory). --- Automorphism. --- Banach space. --- Base change. --- Big O notation. --- Bijection. --- Bilinear form. --- Borel subgroup. --- Cartan subalgebra. --- Cofibration. --- Cohomology. --- Commutative diagram. --- Commutative property. --- Commutator subgroup. --- Complexification (Lie group). --- Conjugacy class. --- Coproduct. --- Coset. --- Cotangent space. --- D-module. --- Derived category. --- Diagram (category theory). --- Differential operator. --- Dimension (vector space). --- Direct image functor. --- Discrete series representation. --- Disk (mathematics). --- Dot product. --- Double coset. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Endomorphism. --- Euler operator. --- Existential quantification. --- Fibration. --- Function space. --- Functor. --- G-module. --- Gelfand pair. --- Generic point. --- Hilbert space. --- Holomorphic function. --- Homomorphism. --- Hyperfunction. --- Ideal (ring theory). --- Infinitesimal character. --- Inner automorphism. --- Invertible sheaf. --- Irreducibility (mathematics). --- Irreducible representation. --- Levi decomposition. --- Lie algebra. --- Line bundle. --- Linear algebraic group. --- Linear space (geometry). --- Manifold. --- Maximal compact subgroup. --- Maximal torus. --- Metric space. --- Module (mathematics). --- Moment map. --- Morphism. --- Noetherian ring. --- Open set. --- Presheaf (category theory). --- Principal series representation. --- Projective line. --- Projective object. --- Projective space. --- Projective variety. --- Reductive group. --- Riemannian geometry. --- Riemann–Hilbert correspondence. --- Right inverse. --- Ring (mathematics). --- Root system. --- Satake diagram. --- Sheaf (mathematics). --- Sheaf of modules. --- Special case. --- Sphere. --- Square-integrable function. --- Sub"ient. --- Subalgebra. --- Subcategory. --- Subgroup. --- Summation. --- Surjective function. --- Symmetric space. --- Symplectic geometry. --- Tensor product. --- Theorem. --- Triangular matrix. --- Vector bundle. --- Volume form. --- Weyl group.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.

Lie groups --- Representations of Lie groups --- Lie groups. --- Representations of Lie groups. --- 512.81 --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- 512.81 Lie groups --- Abelian group. --- Adjoint representation. --- Annihilator (ring theory). --- Atiyah–Singer index theorem. --- Automorphic form. --- Automorphism. --- Cartan subgroup. --- Circle group. --- Class function (algebra). --- Classification theorem. --- Cohomology. --- Commutator subgroup. --- Complete metric space. --- Complex manifold. --- Conjugacy class. --- Cotangent space. --- Dimension (vector space). --- Discrete series representation. --- Dixmier conjecture. --- Dolbeault cohomology. --- Duality (mathematics). --- Eigenvalues and eigenvectors. --- Exponential map (Lie theory). --- Exponential map (Riemannian geometry). --- Exterior algebra. --- Function space. --- Group homomorphism. --- Harmonic analysis. --- Hecke algebra. --- Hilbert space. --- Hodge theory. --- Holomorphic function. --- Holomorphic vector bundle. --- Homogeneous space. --- Homomorphism. --- Induced representation. --- Infinitesimal character. --- Inner automorphism. --- Invariant subspace. --- Irreducibility (mathematics). --- Irreducible representation. --- Isometry group. --- Isometry. --- K-finite. --- Kazhdan–Lusztig polynomial. --- Langlands decomposition. --- Lie algebra cohomology. --- Lie algebra representation. --- Lie algebra. --- Lie group action. --- Lie group. --- Mathematical induction. --- Maximal compact subgroup. --- Measure (mathematics). --- Minkowski space. --- Nilpotent group. --- Orbit method. --- Orthogonal group. --- Parabolic induction. --- Principal homogeneous space. --- Principal series representation. --- Projective space. --- Pseudo-Riemannian manifold. --- Pullback (category theory). --- Ramanujan–Petersson conjecture. --- Reductive group. --- Regularity theorem. --- Representation of a Lie group. --- Representation theorem. --- Representation theory. --- Riemann sphere. --- Riemannian manifold. --- Schwartz space. --- Semisimple Lie algebra. --- Sheaf (mathematics). --- Sign (mathematics). --- Special case. --- Spectral theory. --- Sub"ient. --- Subgroup. --- Support (mathematics). --- Symplectic geometry. --- Symplectic group. --- Symplectic vector space. --- Tangent space. --- Tautological bundle. --- Theorem. --- Topological group. --- Topological space. --- Trivial representation. --- Unitary group. --- Unitary matrix. --- Unitary representation. --- Universal enveloping algebra. --- Vector bundle. --- Weyl algebra. --- Weyl character formula. --- Weyl group. --- Zariski's main theorem. --- Zonal spherical function. --- Représentations de groupes de Lie --- Groupes de lie --- Representation des groupes de lie