Borel-Weil Theorem

Let G=SL(n,C). If lambda in Z^n is the highest weight of an irreducible holomorphic representation V of G, (i.e., lambda is a dominant integral weight), then the G-map phi:V^*->Gamma(lambda) defined by alpha|->F_alpha, where F_alpha(g)=<alpha,gv>, is an isomorphism. Thus, V=Gamma(lambda)^*.

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Huang, J.-S. "The Borel-Weil Theorem." §8.7 in Lectures on Representation Theory. Singapore: World Scientific, pp. 105-107, 1999.

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Borel-Weil Theorem

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Weisstein, Eric W. "Borel-Weil Theorem." From MathWorld--A Wolfram Web Resource.

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