Titlebook: Lie Groups; An Approach through Claudio Procesi Textbook 2007 Springer-Verlag New York 2007 Group representation.algebra.algebraic group.f

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General Methods and Ideas,tematically since most of the interesting examples will appear only in the next chapters. The exposition here is quite far from the classical point of view since we are forced to establish the language in a rather thin general setting. Hopefully this will be repaid in the chapters in which we will treat the interesting results of Invariant Theory.

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Binary Forms,here they all began, the old invariant theory of the 19. century in its most complete achievement: the theory of binary forms. We show a few of the many computational ideas which were developed at that time.

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Symmetric Functions,p some of the very basic theorems on symmetric functions, in part as a way to give a look into 19. century invariant theory, but as well to establish some useful formulas which will show their full meaning only after developing the representation theory of the linear and symmetric groups.

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Group Representations,s. We will use the necessary techniques from elementary algebraic geometry or functional analysis, referring to standard textbooks. One of the main points is a very tight relationship between a special class of algebraic groups, the reductive groups, and compact Lie groups. We plan to illustrate thi

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