Parabolic Subgroups of Algebraic Groups and Induction
David C. Vella
Jan 1986 · American Mathematical Society: Memoirs of the American Mathematical Society Book 347 · American Mathematical Soc.
Ebook
114
Pages
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About this ebook
This paper is a revised version of the author's thesis written under the influence of a long series of papers by E. T. Cline, B. J. Parshall, and L. L. Scott, notably their study of Mackey's imprimitivity theory for algebraic groups. The "CPS" work has emphasized the study of induction and its derived functors, for linear algebraic groups (say, semisimple) over an algebraically closed field of prime characteristic. The author studies in detail the process of induction from one parabolic subgroup [italic]P, followed by restriction to another parabolic subgroup [italic]Q. The author generalizes this Mackey theory from induction to its right derived functors. The main results are too technical to summarize here, but they provide a good foundation for further applications of induction in the representation theory of [italic]G. The author provides many interesting examples, for groups such as SL[subscript]n, to illustrate what can and cannot be achieved with his methods. -- James E. Humphreys.
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