6
votes
0answers
124 views

Zariski closure of orbits of real groups on complex flag manifolds

Let $G$ be a complex reductive algebraic group defined over $\mathbb R$, and $G_0$ its real points. Then the orbits of $G_0$ on $G/B$ need not be real algebraic subvarieties. Take $G=SL_2(\mathbb C)$, ...
7
votes
1answer
554 views

(Real) algebraic geometry for (real) trigonometric polynomials?

Has somebody developed a comprehensive theory of the algebraic structure of trigonometric polynomials in several variables? If yes, where? Background: By a (real) trigonometric polynomial in ...
3
votes
4answers
1k views

Measure on real Grassmannians

OK, so I'm reading about this nice measure you can define on a (real) Grassmannian on Wikipedia. Basically, and to save you the trip through the link, consider the Haar measure $\theta$ on $O(n)$, fix ...