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This invaluable volume collects the expanded lecture notes of thosetutorials. The topics covered include uncertainty principles forlocally compact abelian groups, fundamentals of representations ofp-adic groups, the Harish?Chandra?Howe local characterexpansion, classification of the square-integrable representationsmodulo cuspidal data, Dirac cohomology and Vogan's conjecture,multiplicity-free actions and Schur?Weyl?Howe duality.

p-adic groups. --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Groups, p-adic --- Group theory

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This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.

Probabilities. --- Quantum theory. --- p-adic analysis. --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Kolmogorov Model. --- Quantum Physics. --- Stochastics. --- p-adic Groups.