Frobenius splitting methods in geometry and representation theory / Michel Brion, Shrawan Kumar

This is a truly fantastic book. It is the first comprehensive text on Frobenius splitting and its applications to geometry and representation theory. If this was a one-paragraph review, I would say "buy the book, study it carefully and then apply the contents to a research project''. Written by two of the leading researchers in algebraic groups and representation theory, this book starts with the basic definitions of Frobenius splitting, compatible splittings, etc., and leads the reader carefully and systematically to the latest and most recent applications of these methods. It is extremely well written, and in the beginning the pace is quite slow and builds up as the reader acquires an understanding. It could be used equally well either as a textbook, a reference book or selected portions could be presented in seminars and workshops of varying lengths of time. ... (MathSciNet)