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I am asking about good references (both books and papers) for the well-known Borel–Weil theorem. Thank you very much!

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This question largely duplicates the earlier one on MO 13657. (Also, note the analytic approach in the 2002 AMS graduate text by J.L. Taylor on several complex variables etc.) – Jim Humphreys Feb 28 '12 at 21:54
thank you very much for the AMS graduate text and the analytic approach. I have not noticed it before!I will check it – 314159. Feb 29 '12 at 10:13
Here is a link to the question mentioned in Jim Humphreys' comment above:… – Ricardo Andrade Feb 28 '15 at 17:40
up vote 4 down vote accepted

J.P. Serre: "Représentations linéaires et espaces homogènes kählériens des groupes de Lie compacts (d'après Armand Borel et André Weil)", Séminaire Bourbaki (Paris: Soc. Math. France) 2 (100), 1995, 447–454.

J. Tits: "Sur certaines classes d'espaces homogènes de groupes de Lie, Acad. Roy. Belg. Cl. Sci. Mém. Coll. 29 (1995).

M. Sepanski: Compact Lie groups., Graduate Texts in Mathematics, 235, New York, Springer, 1995. (Theorem 7.58).

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thank you very much, Sepanski's book has a paragraph devoted to Borel-Weil theorem! – 314159. Feb 29 '12 at 10:10

Chapter II.5 in Jantzen's Representations of Algebraic Groups offers an algebraic treatment of this theorem.

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If you're looking for Borel-Weil-Bott theory in positive characteristic, this book is definitely the best exposition I know of. – Chuck Hague Feb 28 '12 at 19:44
many thanks, it is really useful – 314159. Feb 29 '12 at 10:13

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