4 problems

Let $G_\mathbb{R}$ be a semisimple real Lie group, let $\rho$ be a representation of $G_\mathbb{R}$ on a finite-dimensional real vector space $V$, and let…

Let $\mathfrak{g}_{\mathbb{R}}$ be a real form, let $\hat{\mathcal{T}}_{\mathfrak{g}_{\mathbb{R}}}$ be the moduli space of $\mathfrak{g}_{\mathbb{R}}$-complex structures, and let t…

Let $\mathfrak{g}_{\mathbb{R}}$ be a real form with maximal compact subgroup $K_\theta$, let $\mathfrak{a}$ be a Cartan subspace, and let $W(\mathfrak{a})$ be its Weyl group. Real…

Let $G_0$ be a connected complex group viewed as a real Lie group, with complexification $G\cong G_0\times G_0$, maximal compact complex group $K\cong G_0$, and Lie algebra identif…