The Plancherel Theorem for a Reductive Symmetric Space -- The Paley—Wiener Theorem for a Reductive Symmetric Space -- The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space.Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three indepen…
Results on topological spaces -- Rings and modules -- Integral extensions -- Factorial rings -- Field extensions -- Finitely generated algebras -- Gradings and filtrations -- Inductive limits -- Sheaves of functions -- Jordan decomposition and some basic results on groups -- Algebraic sets -- Prevarieties and varieties -- Projective varieties -- Dimension -- Morphisms and dimension -- Tangent s…
Parafree Groups -- The Finitary Andrews-Curtis Conjecture -- Cuts in Kähler Groups -- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries -- Solved and Unsolved Problems Around One Group -- Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators -- Survey on Classifying Spaces for Families of Subgroups -- Are Unitarizable Groups Amenable? -- Probabil…
Gaudin Model and Opers -- Integrable Models with Unstable Particles -- Quantum Reduction in the Twisted Case -- Representation Theory and Quantum Integrability -- Connecting Lattice and Relativistic Models via Conformal Field Theory -- Elliptic Spectral Parameter and Infinite-Dimensional Grassmann Variety -- Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. II -- Weil-Petersson …
Fourier Analysis -- Fourier Series -- Hilbert Spaces -- The Fourier Transform -- Distributions -- LCA Groups -- Finite Abelian Groups -- LCA Groups -- The Dual Group -- Plancherel Theorem -- Noncommutative Groups -- Matrix Groups -- The Representations of SU(2) -- The Peter-Weyl Theorem -- The Heisenberg Group.From the reviews of the first edition: "This lovely book is intended as a primer in h…
Curvature of Contact Metric Manifolds -- A Case for Curvature: the Unit Tangent Bundle -- Convex Hypersurfaces in Hadamard Manifolds -- Contact Metric Geometry of the Unit Tangent Sphere Bundle -- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds -- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds -- Commutative Condition on the S…
I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions.Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxete…
Dirac structures, momentum maps, and quasi-Poisson manifolds -- Construction of Ricci-type connections by reduction and induction -- A mathematical model for geomagnetic reversals -- Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization -- Thompson’s conjecture for real semisimple Lie groups -- The Weinstein conjecture and theorems of nearby and almost exist…
What is Algebra? -- Fields -- Commutative Rings -- Homomorphisms and Ideals -- Modules -- Algebraic Aspects of Dimension -- The Algebraic View of Infinitesimal Notions -- Noncommutative Rings -- Modules over Noncommutative Rings -- Semisimple Modules and Rings -- Division Algebras of Finite Rank -- The Notion of a Group -- Examples of Groups: Finite Groups -- Examples of Groups: Infinite Discre…
Noncommutative Geometry -- Poisson Geometry and Deformation Quantization -- Applications in Physics -- Topological Quantum Field Theory.This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challeng…