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This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups.

512 --- Characters of groups --- Finite fields (Algebra) --- Finite groups --- Groups, Finite --- Group theory --- Modules (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Characters, Group --- Group characters --- Groups, Characters of --- Representations of groups --- Rings (Algebra) --- Algebra --- 512 Algebra --- Finite groups. --- Characters of groups. --- Addition. --- Algebra representation. --- Algebraic closure. --- Algebraic group. --- Algebraic variety. --- Algebraically closed field. --- Bijection. --- Borel subgroup. --- Cartan subalgebra. --- Character table. --- Character theory. --- Characteristic function (probability theory). --- Characteristic polynomial. --- Class function (algebra). --- Classical group. --- Coefficient. --- Cohomology with compact support. --- Cohomology. --- Combination. --- Complex number. --- Computation. --- Conjugacy class. --- Connected component (graph theory). --- Coxeter group. --- Cyclic group. --- Cyclotomic polynomial. --- David Kazhdan. --- Dense set. --- Derived category. --- Diagram (category theory). --- Dimension. --- Direct sum. --- Disjoint sets. --- Disjoint union. --- E6 (mathematics). --- Eigenvalues and eigenvectors. --- Endomorphism. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Fiber bundle. --- Finite field. --- Finite group. --- Fourier transform. --- Green's function. --- Group (mathematics). --- Group action. --- Group representation. --- Harish-Chandra. --- Hecke algebra. --- Identity element. --- Integer. --- Irreducible representation. --- Isomorphism class. --- Jordan decomposition. --- Line bundle. --- Linear combination. --- Local system. --- Mathematical induction. --- Maximal torus. --- Module (mathematics). --- Monodromy. --- Morphism. --- Orthonormal basis. --- P-adic number. --- Parametrization. --- Parity (mathematics). --- Partially ordered set. --- Perverse sheaf. --- Pointwise. --- Polynomial. --- Quantity. --- Rational point. --- Reductive group. --- Ree group. --- Schubert variety. --- Scientific notation. --- Semisimple Lie algebra. --- Sheaf (mathematics). --- Simple group. --- Simple module. --- Special case. --- Standard basis. --- Subset. --- Subtraction. --- Summation. --- Surjective function. --- Symmetric group. --- Tensor product. --- Theorem. --- Two-dimensional space. --- Unipotent representation. --- Vector bundle. --- Vector space. --- Verma module. --- Weil conjecture. --- Weyl group. --- Zariski topology.

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Based on a series of lectures given by Harish-Chandra at the Institute for Advanced Study in 1971-1973, this book provides an introduction to the theory of harmonic analysis on reductive p-adic groups.Originally published in 1979.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.

512.74 --- p-adic groups --- Banach algebras --- Groups, p-adic --- Algebraic groups. Abelian varieties --- p-adic groups. --- 512.74 Algebraic groups. Abelian varieties --- P-adic groups. --- Harmonic analysis. Fourier analysis --- Harmonic analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Group theory --- Harmonic analysis. --- Adjoint representation. --- Admissible representation. --- Algebra homomorphism. --- Algebraic group. --- Analytic continuation. --- Analytic function. --- Associative property. --- Automorphic form. --- Automorphism. --- Banach space. --- Bijection. --- Bilinear form. --- Borel subgroup. --- Cartan subgroup. --- Central simple algebra. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Class function (algebra). --- Commutative property. --- Compact space. --- Composition series. --- Conjugacy class. --- Corollary. --- Dimension (vector space). --- Discrete series representation. --- Division algebra. --- Double coset. --- Eigenvalues and eigenvectors. --- Endomorphism. --- Epimorphism. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Factorization. --- Fourier series. --- Function (mathematics). --- Functional equation. --- Fundamental domain. --- Fundamental lemma (Langlands program). --- G-module. --- Group isomorphism. --- Haar measure. --- Hecke algebra. --- Holomorphic function. --- Identity element. --- Induced representation. --- Inner automorphism. --- Lebesgue measure. --- Levi decomposition. --- Lie algebra. --- Locally constant function. --- Locally integrable function. --- Mathematical induction. --- Matrix coefficient. --- Maximal compact subgroup. --- Meromorphic function. --- Module (mathematics). --- Module homomorphism. --- Open set. --- Order of integration (calculus). --- Orthogonal complement. --- P-adic number. --- Pole (complex analysis). --- Product measure. --- Projection (linear algebra). --- Quotient module. --- Quotient space (topology). --- Radon measure. --- Reductive group. --- Representation of a Lie group. --- Representation theorem. --- Representation theory. --- Ring homomorphism. --- Schwartz space. --- Semisimple algebra. --- Separable extension. --- Sesquilinear form. --- Set (mathematics). --- Sign (mathematics). --- Square-integrable function. --- Sub"ient. --- Subalgebra. --- Subgroup. --- Subset. --- Summation. --- Support (mathematics). --- Surjective function. --- Tempered representation. --- Tensor product. --- Theorem. --- Topological group. --- Topological space. --- Topology. --- Trace (linear algebra). --- Transitive relation. --- Unitary representation. --- Universal enveloping algebra. --- Variable (mathematics). --- Vector space. --- Analyse harmonique (mathématiques)

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The editors of this Special Issue titled “Intelligent Control in Energy Systems” have attempted to create a book containing original technical articles addressing various elements of intelligent control in energy systems. In response to our call for papers, we received 60 submissions. Of those submissions, 27 were published and 33 were rejected. In this book, we offer the 27 accepted technical articles as well as one editorial. Authors from 15 countries (China, Netherlands, Spain, Tunisia, United Sates of America, Korea, Brazil, Egypt, Denmark, Indonesia, Oman, Canada, Algeria, Mexico, and the Czech Republic) elaborate on several aspects of intelligent control in energy systems. The book covers a broad range of topics including fuzzy PID in automotive fuel cell and MPPT tracking, neural networks for fuel cell control and dynamic optimization of energy management, adaptive control on power systems, hierarchical Petri Nets in microgrid management, model predictive control for electric vehicle battery and frequency regulation in HVAC systems, deep learning for power consumption forecasting, decision trees for wind systems, risk analysis for demand side management, finite state automata for HVAC control, robust ?-synthesis for microgrids, and neuro-fuzzy systems in energy storage.

energy management system --- artificial neural network --- control architecture --- intelligent buildings --- sensitivity analysis --- neural networks --- active balance --- photovoltaic system --- fast frequency response --- artificial intelligence --- MPPT operation --- model uncertainty --- load frequency control --- decision tree --- multi-agent control --- hybrid power plant --- Fault Ride Through Capability --- optimization --- small scale compressed air energy storage (SS-CAES) --- smart micro-grid --- current distortion --- hybrid electric vehicle --- parameter estimation --- railway --- ANFIS --- solar monitoring system --- urban microgrids --- phase-load balancing --- model reduction --- high-speed railway --- energy internet --- coordination of reserves --- differential evolution --- photovoltaic array --- ancillary service --- adjacent areas --- instantaneous optimization minimum power loss --- model predictive control --- HVAC systems --- sliding mode control --- MPPT: maximum power point tracking --- power oscillations --- thyristor --- interaction minimization --- occupancy model --- fuzzy logic controller --- power transformer winding --- RLS --- integrated energy systems --- vibration characteristics --- battery safety --- error estimation --- error compensation --- static friction --- convolutional neural network --- forecasting --- continuous voltage control --- medium voltage --- bridgeless SEPIC PFC converter --- building climate control --- PEM fuel cell --- proton exchange membrane fuel cell --- compound structured permanent-magnet motor --- occupancy-based control --- four phases interleaved boost converter --- long short term memory --- line switching --- lithium-ion battery pack --- back propagation (BP) neural network --- doubly-fed induction generator --- double forgetting factors --- current controller design --- repetitive controller --- exhaust gas recirculation (EGR) valve system --- neural network controller --- step-up boost converter --- internal short circuit resistance --- electric power consumption --- electric vehicle --- multiphysical field analysis --- energy efficiency --- multi-energy complementary --- system identification --- ?-synthesis --- network sensitivity --- intelligent control --- ?-class function --- frequency support --- multi-step forecasting --- frequency containment reserve --- orthogonal least square --- rule-based control --- industrial process --- hierarchical Petri nets --- wind integrated power system --- probabilistic power flow --- voltage controlling --- adaptive backstepping --- AC-DC converters --- line loss --- demand side management --- energy systems --- short-circuit experiment --- winding-fault characteristics --- neutral section --- stochastic power system operating point drift --- neural network algorithm --- operation limit violations --- fractional order fuzzy PID controller --- preventive control --- AC static switch --- battery packs --- model-based fault detection --- automotive application --- nonlinear power systems --- adaptive damping control --- pilot point --- energy management --- position control --- frequency control dead band --- fuzzy --- voltage violations --- distribution network planning --- frequency regulation --- energy management strategy --- multiple-point control --- electric meter --- polynomial expansion --- commercial/residential buildings --- system modelling --- three-stage --- soft internal short circuit --- demand response