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This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Nilpotent Lie groups. --- Lie groups, Nilpotent --- Lie groups --- Nilpotent groups --- Topological groups. --- Lie groups. --- Topological Groups, Lie Groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups

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This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis. Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis. Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis.

Electronic books. -- local. --- Harmonic analysis. --- Nilpotent Lie groups. --- Harmonic analysis --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Lie groups, Nilpotent --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Group theory. --- Approximation theory. --- Fourier analysis. --- Functions of complex variables. --- Mathematical models. --- Abstract Harmonic Analysis. --- Fourier Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Approximations and Expansions. --- Several Complex Variables and Analytic Spaces. --- Group Theory and Generalizations. --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Lie groups --- Nilpotent groups --- Differential equations, partial. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Partial differential equations --- Math --- Science --- Analysis, Fourier --- Complex variables --- Elliptic functions --- Functions of real variables --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Models, Mathematical --- Simulation methods