I am struggling with understanding the motivation for both the classical and geometric forms of Satake equivalence. What prompted the development of this equivalence? Any open problems that it was trying to solve during that time?
Also, both the classical and geometric forms of Satake equivalence are very challenging for me - I can't really seem to properly get my head around it. Are you guys also able to provide an interpretation on what exactly this equivalence is meant to show?
Any contributions would be greatly appreciated as I am having a really hard time with this :/