Lecture 7: Category O and Representations of Algebraic Groups
نویسنده
چکیده
We continue our study of the representation theory of a finite dimensional semisimple Lie algebra g by introducing and studying the category O of g-modules that has appeared in the seminal paper by Bernstein, Israel and Sergei Gelfand, [BGG]. We establish a block decomposition for this category and use this to prove the Weyl character formula for finite dimensional irreducible g-modules. Then we proceed to studying the representations of reductive algebraic groups both in zero and positive characteristic. Our main result is the classification of irreducible rational representations.
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تاریخ انتشار 2015