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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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    $\begingroup$ 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.) $\endgroup$
    – Jim Humphreys
    Commented Feb 28, 2012 at 21:54
  • $\begingroup$ thank you very much for the AMS graduate text and the analytic approach. I have not noticed it before!I will check it $\endgroup$
    – 314159.
    Commented Feb 29, 2012 at 10:13
  • $\begingroup$ Here is a link to the question mentioned in Jim Humphreys' comment above: mathoverflow.net/questions/13657/… $\endgroup$
    – Ricardo Andrade
    Commented Feb 28, 2015 at 17:40

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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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  • $\begingroup$ thank you very much, Sepanski's book has a paragraph devoted to Borel-Weil theorem! $\endgroup$
    – 314159.
    Commented Feb 29, 2012 at 10:10
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Chapter II.5 in Jantzen's Representations of Algebraic Groups offers an algebraic treatment of this theorem.

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  • $\begingroup$ If you're looking for Borel-Weil-Bott theory in positive characteristic, this book is definitely the best exposition I know of. $\endgroup$
    – Chuck Hague
    Commented Feb 28, 2012 at 19:44

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