Spherical amoebae and a spherical logarithm map
Spherical amoebae and a spherical logarithm map
Let $G$ be a connected reductive algebraic group over $\mathbb{C}$ with a maximal compact subgroup $K$. Let $G/H$ be a (quasi-affine) spherical homogeneous space. In the first part of the paper, following Akhiezer's definition of spherical functions, we introduce a $K$-invariant map $sLog_{\Gamma, t}: G/H \to \mathbb{R}^s$ which depends on …