Return to Answer

I think this might be so standard that there is no obvious reference. The cohomology has a basis of Schubert classes. In the adjoint case, Schubert classes are indexed by the Weyl group orbit of the highest weight of the adjoint module. This is the set of long roots, or in the simply laced case, by all roots, implying, in particular, the claim on the Euler characteristic.

P.S. If you really would like a printed reference to cite, I found one for you: Fact 2.8(ii) in P.E. Chaput, N. Perrin, On the quantum cohomology of adjoint varieties, Proceedings of the London Mathematical Society, Volume 103, Issue 2, August 2011, Pages 294–330.

I think this might be so standard that there is no obvious reference. The cohomology has a basis of Schubert classes. In the adjoint case, Schubert classes are indexed by the Weyl group orbit of the highest weight of the adjoint module. This is the set of long roots, or in the simply laced case, of all roots, implying, in particular, the claim on the Euler characteristic.

P.S. If you really would like a printed reference to cite, I found one for you: Fact 2.8(ii) in P.E. Chaput, N. Perrin, On the quantum cohomology of adjoint varieties, Proceedings of the London Mathematical Society, Volume 103, Issue 2, August 2011, Pages 294–330.

I think this might be so standard that there is no obvious reference. The cohomology has a basis of Schubert classes. In the adjoint case, Schubert classes are indexed by the Weyl group orbit of the weight of the adjoint module. This is the set of long roots, or in the simply laced case, by all roots, implying, in particular, the claim on the Euler characteristic.

P.S. If you really would like a printed reference to cite, I found one for you: Fact 2.8(ii) in P.E. Chaput, N. Perrin, On the quantum cohomology of adjoint varieties, Proceedings of the London Mathematical Society, Volume 103, Issue 2, August 2011, Pages 294–330.

I think this might be so standard that there is no obvious reference. The cohomology has a basis of Schubert classes. In the adjoint case, Schubert classes are indexed by the Weyl group orbit of the highest weight of the adjoint module. This is the set of long roots, or in the simply laced case, by all roots, implying, in particular, the claim on the Euler characteristic.

P.S. If you really would like a printed reference to cite, I found one for you: Fact 2.8(ii) in P.E. Chaput, N. Perrin, On the quantum cohomology of adjoint varieties, Proceedings of the London Mathematical Society, Volume 103, Issue 2, August 2011, Pages 294–330.

I think this might be so standard that there is no obvious reference. The cohomology has a basis of Schubert classes. In the adjoint case, Schubert classes are indexed by the Weyl group orbit of the weight of the adjoint module. This is the set of long roots, or in the simply laced case, by all roots, implying, in particular, the claim on the Euler characteristic.

I think this might be so standard that there is no obvious reference. The cohomology has a basis of Schubert classes. In the adjoint case, Schubert classes are indexed by the Weyl group orbit of the weight of the adjoint module. This is the set of long roots, or in the simply laced case, by all roots, implying, in particular, the claim on the Euler characteristic.

P.S. If you really would like a printed reference to cite, I found one for you: Fact 2.8(ii) in P.E. Chaput, N. Perrin, On the quantum cohomology of adjoint varieties, Proceedings of the London Mathematical Society, Volume 103, Issue 2, August 2011, Pages 294–330.