Representation Theory of Lie Groups

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AbstractSahiThe project envisages investigations in three different areas within the broad framework of representation theory. The first set of questions is related to Kontsevich's deformation quantization and its connections with Lie theory. The second area of investigation is the study of possible generalizations of the theta-correspondence via explicit models of small unitary representations and the study of their tensor products. The third topic of research is the Macdonald-Cherednik theory of multivariate special functions.Representation theory is a central discipline in modern mathematics and is therefore inspired by questions that arise naturally in diverse subjects such as algebra, analysis, number theory and physics. Roughly speaking whenever a mathematical problem possesses a group of symmetries, the representation theory of the group plays a potentially key role in the considerations. Indeed, the seeds of the subject lie in the work of Galois on the symmetries of polynomial equations; of Spohus Lie on the symmetries of differential equations; and of Newton, Fourier, Einstein, Wigner and others on the symmetries of physical systems.