Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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

share|improve this question
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: mathoverflow.net/questions/13657/… –  Ricardo Andrade Feb 28 at 17:40

2 Answers 2

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).

share|improve this answer
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.

share|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.