User - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T15:02:44Z http://mathoverflow.net/feeds/user/3649 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/13657/proof-of-borel-weil-bott-theorem Proof of Borel-Weil-Bott Theorem unknown (google) 2010-02-01T10:56:35Z 2010-03-22T19:39:02Z <p>Is there any purely algebraic proof of Borel-Weil-Bott theorem. I mean only techniques from Algebraic group. In each and every proof I have seen so far they use Lie group techniques and then translate to Algebraic group version. I need a proper reference which is easily readable.</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/13477/normality-of-an-affine-semigroup Normality of an affine semigroup unknown (google) 2010-01-30T16:06:21Z 2010-02-06T18:26:22Z <p>An affine monoid is a finitely generated commutative submonoid of $\mathbb Z^k$ for some positive integer k. Let S be an affine monoid and let G(S) be the group generated by S. We say the monoid S is normal if and only if for all $g \in G(S)$ and $n \in \mathbb N \setminus {0}$, $ng \in S$ implies $g \in S$. </p> <p>Let $S$ be the submonoid generated by the finite set <code>$T= \{(p_0,p_1, \cdots ,p_{n-1}) \in (\mathbb Z_{\geq 0})^n: \sum_{i=0}^{n-1}p_i=n \,\, and \,\, \sum_{i=0}^{n-1}i.p_i \cong 0 \pmod n\}$</code>. Now my question is how to prove that $S$ is normal ?</p> http://mathoverflow.net/questions/13477/normality-of-an-affine-semigroup/13879#13879 Comment by 2010-02-03T08:45:08Z 2010-02-03T08:45:08Z Thanks for your answer. Actually I want to prove EGZ theorem using this result, so I do not want to use EGZ to prove this result. I knew this proof already. http://mathoverflow.net/questions/13477/normality-of-an-affine-semigroup/13496#13496 Comment by 2010-01-30T20:11:49Z 2010-01-30T20:11:49Z Yes, I was thinking the same as well. (1,0,1,0) is not in G(S). By the way how to prove for n is a prime ?