Nearly a century after the expropriation, in 1975, the US court of claims described the US government's conduct thus: "A more ripe and rank case of dishonorable dealings will never, in all probability, be found in our history".
The Great Sioux Reservation, formed in the eighteen-sixties, shrunk again and again in 1980, a federal court said, of the whole sad story, "a more ripe and rank case of dishonorable dealings will never, in all probability, be found in our history".
More than 100 years later, in 1979, the United States Court of Claims, discussing the federal government's misdeeds against the Sioux, including its tactic of starving them, before it appropriated the land, wrote that "a more ripe and rank case of dishonorable dealing will never, in all probability, be found in our history".
Here we present the latter case in detail, describing features which will be also important for the general rank case.
In the general higher rank case, the integral formulas are applied to find asymptotic estimates for the spherical functions.
Accordingly, results derived in literature may not be applicable since they are derived for the full rank case.
In the higher rank case we prove moreover that heat not only concentrates in an annulus but also along the (K-orbit) of the ϱ-axis.
When X=C one recovers the "H−2-construction" of Kiselev and Simon and so, to some extent, our results can be regarded as an extension of it to the infinite rank case.
There are a few notions of singular Hermitian metrics for vector bundles of higher rank, but the theory of singular Hermitian metrics, while rather developed for line bundles, is much less developed in the higher rank case.
In 1980, more than a century later, the US Supreme Court ruled in favor of the Sioux, claiming "a more ripe and rank case of dishonorable dealings will never, in all probability, be found in our history".
