Lie groups beyond an introduction
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Publication:5917426
zbMath1075.22501MaRDI QIDQ5917426
Publication date: 6 January 2003
Published in: Progress in Mathematics (Search for Journal in Brave)
Semisimple Lie groups and their representations (22E46) General properties and structure of real Lie groups (22E15) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups (22-01)
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sets of finite perimeter in Carnot groups: existence of a tangent hyperplane ⋮ Classification of Klein four symmetric pairs of holomorphic type for \(\text{E}_{7(-25)}\) ⋮ Extended Vogan diagrams ⋮ Equivariant de Rham cohomology: theory and applications ⋮ Matrix elements of irreducible representations of \(\mathrm{GL} (n + 1) \times\mathrm{GL} (n + 1)\) and multivariable matrix-valued orthogonal polynomials ⋮ Fock-Goncharov coordinates for rank two Lie groups ⋮ Equal rank real forms of affine non-twisted Kac-Moody Lie superalgebras ⋮ Spectral uniqueness of bi-invariant metrics on symplectic groups ⋮ Conformal actions of real-rank 1 simple Lie groups on pseudo-Riemannian manifolds ⋮ On cohomogeneity one linear actions on pseudo-Euclidean space \(\mathbb{R}^{p , q} \) ⋮ Flat compact Hermite-Lorentz manifolds in dimension 4 ⋮ The length and depth of compact Lie groups ⋮ Quasi-isometric bounded generation by \(\mathbb{Q}\)-rank-one subgroups ⋮ The structure theory of nilspaces. III: Inverse limit representations and topological dynamics ⋮ The automorphism group and limit set of a bounded domain I: the finite type case ⋮ Quaternionic hyperbolic Kleinian groups with commutative trace skew-fields ⋮ On the Hirzebruch-Kobayashi-Ono proportionality principle and the non-existence of compact solvable Clifford-Klein forms of certain homogeneous spaces ⋮ Convexity properties of gradient maps associated to real reductive representations ⋮ Real hypersurfaces in the complex hyperbolic quadric with Reeb parallel structure Jacobi operator ⋮ Contact real hypersurfaces in the complex hyperbolic quadric ⋮ Polarized relations on horizontal \(\operatorname{SL}(2)\)'s ⋮ Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations ⋮ Non-isometric Riemannian \(G\)-manifolds with equal equivariant spectra ⋮ Schottky groups acting on homogeneous rational manifolds ⋮ Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds ⋮ Complex adjoint orbits in Lie theory and geometry ⋮ The Hausdorff-Young inequality on Lie groups ⋮ Matrix spherical analysis on nilmanifolds ⋮ Closed \({\mathrm{G}}_2\)-structures on non-solvable Lie groups ⋮ The complex-time Segal-Bargmann transform ⋮ Affine actions with Hitchin linear part ⋮ Comparison and continuity of Wick-type star products on certain coadjoint orbits ⋮ The parameter space of orbits of a maximal compact subgroup acting on a flag manifold ⋮ Invariant solutions of the wave equation on static spherically symmetric spacetimes admitting \(G_7\) isometry algebra ⋮ Spherical representations of Lie supergroups ⋮ Leading weight vectors and homomorphisms between generalized Verma modules ⋮ Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series ⋮ Wave equation for sums of squares on compact Lie groups ⋮ An effective Ratner equidistribution result for SL\((2,\mathbb R)\ltimes \mathbb R^2\) ⋮ \(C^\ast\)-algebraic intertwiners for principal series: case of \(\mathrm{SL}(2)\) ⋮ A generalised Gangolli-Lévy-Khintchine formula for infinitely divisible measures and Lévy processes on semi-simple Lie groups and symmetric spaces ⋮ Hermitian real forms of contragredient Lie superalgebras ⋮ A linearization of quantum channels ⋮ Invariant solutions to the Strominger system on complex Lie groups and their quotients ⋮ Bourgain-Brezis inequalities on symmetric spaces of non-compact type ⋮ Stable branching rules for classical symmetric pairs ⋮ Vogan duality for nonlinear type B ⋮ Classification of solutions to Toda systems of types \(C\) and \(B\) with singular sources ⋮ Corwin–Greenleaf multiplicity function for compact extensions of ℝn ⋮ Different faces of the shearlet group ⋮ Strong property (T) for higher-rank simple Lie groups: Figure 1. ⋮ Signature characters of invariant Hermitian forms on irreducible Verma modules and Hall-Littlewood polynomials ⋮ Classification of minimal representations of real simple Lie groups ⋮ Maximal \(\mathsf{Sp}(4,\mathbb R)\) surface group representations, minimal immersions and cyclic surfaces ⋮ On entropy, regularity and rigidity for convex representations of hyperbolic manifolds ⋮ A Concise Parametrization of Affine Transformation ⋮ ON THE EXACTNESS OF KOSTANT–KIRILLOV FORM AND THE SECOND COHOMOLOGY OF NILPOTENT ORBITS ⋮ Multiplicity function for tensor powers of modules of the \(A_n\) algebra ⋮ Nearly holomorphic sections on compact Hermitian symmetric spaces ⋮ Parabolic induction and restriction via -algebras and Hilbert -modules ⋮ A generalized Harish-Chandra method of descent for reductive Lie algebras ⋮ Special values for conformally invariant systems associated to maximal parabolics of quasi-Heisenberg type ⋮ A refinement of strong multiplicity one for spectra of hyperbolic manifolds ⋮ An analogue of Weyl’s law for quantized irreducible generalized flag manifolds ⋮ A generalization of Cachazo-Douglas-Seiberg-Witten conjecture for symmetric spaces ⋮ The Levi problem on strongly pseudoconvex \(G\)-bundles ⋮ Continuity of the Mackey-Higson bijection ⋮ Octonion-valued forms and the canonical 8-form on Riemannian manifolds with a Spin(9)-structure ⋮ \(G\)-Sasaki manifolds and K-energy ⋮ Ricci soliton and pseudo-Einstein real hypersurfaces in the complex hyperbolic quadric ⋮ The spin group in superspace ⋮ Symplectic symmetric pairs of contragredient Lie superalgebras ⋮ Gelfand-Kirillov dimensions of the ℤ-graded oscillator representations of 𝔬(n,ℂ) and 𝔰𝔭(2n,ℂ) ⋮ The density theorem for discrete series representations restricted to lattices ⋮ Ricci-Bourguignon solitons on real hypersurfaces in the complex hyperbolic quadric ⋮ Explicit inner product formulas and Bessel period formulas for HST lifts ⋮ Almost Kähler geometry of adjoint orbits of semisimple Lie groups ⋮ Fractional Laplacians and extension problems: The higher rank case ⋮ Weight multiplicity formulas for bivariate representations of classical Lie algebras ⋮ Invariant Gaussian fields on homogeneous spaces: explicit constructions and mean nodal volume ⋮ THE TWISTED TENSOR L-FUNCTION OF GSp4 ⋮ Cyclic structure Jacobi semi-symmetric real hypersurfaces in the complex quadric ⋮ Stability, analytic stability for real reductive Lie groups ⋮ Partial Dirac cohomology and tempered representations ⋮ Equality of the algebraic and geometric ranks of Cartan subalgebras and applications to linearization of a system of ordinary differential equations ⋮ Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie groups ⋮ Outer automorphism groups of real forms of contragredient Lie superalgebras ⋮ A generating function for Blattner’s formula ⋮ Affine Killing Reeb vector field for a real hypersurface in the complex quadric ⋮ Count lifts of non-maximal closed horocycles on \(SL_N(\mathbb{Z}) \backslash SL_N(\mathbb{R})/SO_N({\mathbb{R}})\) ⋮ On the classification of 3-dimensional complex hom-Lie algebras ⋮ Iwahori-Hecke algebra and unramified local \(L\)-functions ⋮ Multiplicity formulas for fundamental strings of representations of classical Lie algebras ⋮ Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters ⋮ Geometric classification of semidirect products in the maximal parabolic subgroup of Sp(2, ℝ) ⋮ Abelianization of Higgs bundles for quasi-split real groups ⋮ Optimal Control Problems with Symmetry Breaking Cost Functions ⋮ Coadjoint orbits in duals of Lie algebras with admissible ideals ⋮ Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties ⋮ Galois representations for general symplectic groups ⋮ Real forms of complex Lie superalgebras and supergroups ⋮ INVARIANT DIFFERENTIAL OPERATORS FOR NON-COMPACT LIE GROUPS: PARABOLIC SUBALGEBRAS ⋮ Lie Theory for Quantum Control ⋮ A canonical distribution on isoparametric submanifolds I ⋮ Kähler–Einstein Metrics on Toric Manifolds and G-manifolds ⋮ Double Vogan diagrams and semisimple symmetric spaces ⋮ Actions of semisimple Lie groups preserving a degenerate Riemannian metric ⋮ Morse and Lyapunov spectra and dynamics on flag bundles ⋮ Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups ⋮ CONSTRUCTION OF CERTAIN FUZZY FLAG MANIFOLDS ⋮ GRADIENT FLOWS FOR OPTIMIZATION IN QUANTUM INFORMATION AND QUANTUM DYNAMICS: FOUNDATIONS AND APPLICATIONS ⋮ Multiplicity bounds and the subrepresentation theorem for real spherical spaces ⋮ Wavelets onS3andSO(3)-Their construction, relation to each other and Radon transform of wavelets onSO(3) ⋮ Spin norm, pencils, and the u-small convex hull ⋮ How to pick a random integer matrix? (and other questions) ⋮ Harmonic morphisms from the compact semisimple Lie groups and their non-compact duals ⋮ Index and Cartan decomposition of a real semisimple Lie algebra. ⋮ A Lie algebra method for rational parametrization of Severi-Brauer surfaces. ⋮ Isoparametric foliations on complex projective spaces ⋮ Schubert varieties as variations of Hodge structure ⋮ Matsumoto–Yor Process and Infinite Dimensional Hyperbolic Space ⋮ Power-law distributions for the free path length in Lorentz gases ⋮ On Ky Fan's result on eigenvalues and real singular values of a matrix ⋮ WHITE NOISE ANALYSIS ON MANIFOLDS AND THE ENERGY REPRESENTATION OF A GAUGE GROUP ⋮ On the kernel of the maximal flat Radon transform on symmetric spaces of compact type ⋮ Maximal abelian subgroups of compact simple Lie groups of type E ⋮ On the spectrum of $(Spin(10,2),SL(2,\mathbb{R}))$ in $E_{7,3}$ ⋮ Representations of Lie groups and random matrices ⋮ Mumford-Tate groups of polarizable Hodge structures ⋮ A new classification on parallel Ricci tensor for real hypersurfaces in the complex quadric ⋮ Coloring the Voronoi tessellation of lattices ⋮ Flat Nonunimodular Lorentzian Lie Algebras ⋮ LIFTING TO GL(2) OVER A DIVISION QUATERNION ALGEBRA, AND AN EXPLICIT CONSTRUCTION OF CAP REPRESENTATIONS ⋮ Dolbeault cohomology of nilmanifolds with left-invariant complex structure ⋮ Rigidity of the Weyl chamber flow, and vanishing theorems of Matsushima and Weil ⋮ Methods of computing Campbell-Hausdorff formula ⋮ On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras ⋮ Finite order automorphisms on real simple Lie algebras ⋮ Construction of the Noncommutative Rank I Bergman Domain ⋮ TSALLIS ENTROPY COMPOSITION AND THE HEISENBERG GROUP ⋮ Symmetry principles in quantum systems theory ⋮ MAXIMAL COMPACT SUBGROUPS IN THE O-MINIMAL SETTING ⋮ The Images of Restriction Maps and Dirac Cohomology ⋮ Higgs bundles for real groups and the Hitchin–Kostant–Rallis section ⋮ A reducible Weil representation of sp(4) realized by differential operators in the space of smooth functions on H2 × S1 ⋮ Symplectic Dirac cohomology and lifting of characters to metaplectic groups ⋮ Character sheaves for classical symmetric pairs ⋮ Homogeneous Lagrangian foliations on complex space forms ⋮ The algebraic Mackey-Higson bijections ⋮ Gradient flows for the minimum distance to the sum of adjoint orbits ⋮ Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8 ⋮ Real hypersurfaces in the complex hyperbolic quadric with normal Jacobi operator of Codazzi type ⋮ The cohomology of semi-simple Lie groups, viewed from infinity ⋮ Characters of irreducible unitary representations of 𝑈(𝑛,𝑛+1) via double lifting from 𝑈(1) ⋮ Positivity of principal matrix coefficients of principal series representations of $GL_{n}(R)$ ⋮ Isometric actions of quaternionic symplectic groups ⋮ Irreducible Characters and Semisimple Coadjoint Orbits ⋮ Unnamed Item ⋮ Unnamed Item ⋮ C1 actions on manifolds by lattices in Lie groups ⋮ On Computing Linearizing Coordinates From Symmetry Algebra ⋮ The structure of almost Abelian Lie algebras ⋮ Unnamed Item ⋮ Limiting Sobolev and Hardy inequalities on stratified homogeneous groups ⋮ Geometric orbital integrals and the center of the enveloping algebra ⋮ Distal Actions of Automorphisms of Lie Groups G on SubG ⋮ Lower bounds for Maass forms on semisimple groups ⋮ Unnamed Item ⋮ Strong multiplicity one theorems for locally homogeneous spaces of compact-type ⋮ Hermitian curvature flow on unimodular Lie groups and static invariant metrics ⋮ Pointwise equidistribution for one parameter diagonalizable group action on homogeneous space ⋮ Toeplitz Operators on the Domain $$\{Z\in M_{2\times 2}(\mathbb {C}) \mid Z Z^* < I\}$$ with $$\mathrm {U}(2)\times \mathbb {T}^2$$ -Invariant Symbols ⋮ SOLVABLE LIE GROUPS DEFINABLE IN O-MINIMAL THEORIES ⋮ Classification of horizontal s ⋮ A GLUING FORMULA FOR THE ANALYTIC TORSION ON HYPERBOLIC MANIFOLDS WITH CUSPS ⋮ The dancing metric, ${G}_2$-symmetry and projective rolling ⋮ Markov random walks on homogeneous spaces and Diophantine approximation on fractals ⋮ Complex quantum groups and a deformation of the Baum–Connes assembly map ⋮ Variations on a Theorem of Tate ⋮ Profinite invariants of arithmetic groups ⋮ Lie theory and the Chern–Weil homomorphism ⋮ Low degree representations of simple Lie groups ⋮ An effective equidistribution result for SL(2,R)⋉(R2)⊕k and application to inhomogeneous quadratic forms ⋮ A NEW CLASSIFICATION OF REAL HYPERSURFACES WITH REEB PARALLEL STRUCTURE JACOBI OPERATOR IN THE COMPLEX QUADRIC ⋮ Gradings for nilpotent Lie algebras ⋮ The central limit theorem for eigenvalues ⋮ Spherical functions on spheres of rank two ⋮ A second adjoint theorem for \SL(2,ℝ) ⋮ VOGAN DIAGRAMS OF UNTWISTED AFFINE KAC–MOODY SUPERALGEBRAS ⋮ DECOMPOSITION THEOREMS FOR AUTOMORPHISM GROUPS OF TREES ⋮ On sums of admissible coadjoint orbits ⋮ The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras ⋮ Symmetry analysis of wave equation on static spherically symmetric spacetimes with higher symmetries ⋮ THE CRITICAL VALUES OF RANKIN–SELBERG CONVOLUTIONS ⋮ On commutative homogeneous vector bundles attached to nilmanifolds ⋮ Wave front sets of reductive Lie group representations II ⋮ Some remarks on Richardson orbits in complex symmetric spaces ⋮ Poisson structures on complex flag manifolds associated with real forms ⋮ Sub-Riemannian Geometry and Hypoelliptic Operators ⋮ Combinatorics-Based Approaches to Controllability Characterization for Bilinear Systems ⋮ Polynomial-time Classification of Skew-symmetrizable Matrices with a Positive Definite Quasi-Cartan Companion ⋮ Contragredient supersymmetric pairs ⋮ Skew-symmetric endomorphisms in M1,3 : a unified canonical form with applications to conformal geometry ⋮ The Bogomolov multiplier of Lie algebras ⋮ The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds ⋮ Skew-symmetric endomorphisms in M1,n : a unified canonical form with applications to conformal geometry ⋮ Riemannian manifolds with local symmetry ⋮ On the Real Forms of the Exceptional Lie Algebra 𝔢 6 $$\mathfrak{e}_{6}$$ and Their Satake Diagrams ⋮ Real structures on nilpotent orbit closures ⋮ Unnamed Item ⋮ Boundary orbit strata and faces of invariant cones and complex Ol’shanskiĭ semigroups ⋮ Vanishing of cohomology and parameter rigidity of actions of solvable Lie groups, II ⋮ The Lie algebra of derivations of a current Lie algebra ⋮ Measures and entropy on non compact dynamics ⋮ The Anomaly flow on unimodular Lie groups ⋮ Discretely decomposable restrictions of (𝔤,K)-modules for Klein four symmetric pairs of exceptional Lie groups of Hermitian type ⋮ Warped Riemannian Metrics for Location-Scale Models ⋮ Extending the Action of Schottky Groups on the Complex Anti-de Sitter Space to the Projective Space ⋮ Cartan subgroups and regular points of o‐minimal groups ⋮ ON MEASURE TRANSITIVE G-SETS ⋮ Coadjoint Orbits of Certain Motion Groups and Their Coherent States ⋮ Classification of spherical algebraic subalgebras of real simple Lie algebras of rank 1 ⋮ Stability of Asai local factors for GL(2) ⋮ Real structures on symmetric spaces ⋮ Shrinking target problems for flows on homogeneous spaces ⋮ The joint spectrum ⋮ A geometric formula for multiplicities of 𝐾-types of tempered representations ⋮ Some remarks on representations of Yang-Mills algebras ⋮ The noncommutative Poisson bracket and the deformation of the family algebras ⋮ Outer invariance entropy for discrete-time linear systems on Lie groups ⋮ Indecomposable representations of the Diamond Lie algebra ⋮ TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS ⋮ A criterion for discrete branching laws for Klein four symmetric pairs and its application to E6(−14) ⋮ On Borel–de Siebenthal Representations ⋮ The automorphism group and limit set of a bounded domain II: the convex case ⋮ Transgression in bounded cohomology and a conjecture of Monod ⋮ Lie theory for asymptotic symmetries in general relativity: The BMS group ⋮ Bohr density of simple linear group orbits ⋮ Analytic Torsion and Dynamical Flow:A Survey on the Fried Conjecture ⋮ A proof of Casselman’s comparison theorem ⋮ Cofinite proper classifying spaces for lattices in semisimple lie groups of R-rank 1 ⋮ Dirac Cohomology and Generalization of Classical Branching Rules ⋮ COMPACT ORBITS OF PARABOLIC SUBGROUPS ⋮ Real hypersurfaces in the complex hyperbolic quadric with Reeb invariant Ricci tensor ⋮ Approximation of nilpotent orbits for simple Lie groups
