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 $G=SL_2(\mathbb C)$, ...
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 ...
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 ...
This question is predicated on my understanding that real algebraic geometry (henceforth RAG) is the version of algebraic geometry (AG) one gets when replacing (esp. algebraically closed) fields with ...