Wikipedia defines the Harish Chandra function on a semisimple Lie group to be $$g\mapsto \int_Ka(kg)^\rho dk$$ where $K$ is a maximal compact subgroup, $a(g)$ is the $A$ factor in the Iwasawa decomposition of $g$ and $\rho$ is the Weyl vector (half the sum of the positive roots). What does it mean to put that vector in the superscript?
https://en.wikipedia.org/wiki/Harish-Chandra%27s_%CE%9E_function