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Jan 23, 2011 at 6:52 comment added Ben Webster One thing that seems worth mentioning: the affine Grassmannian is analogous to spaces studied a lot by number theorists; replace $\mathbb C$ by a finite field $\mathbb F$ and suddenly what you're looking at is the group over the local field $\mathbb F((t))$ modulo its maximal compact. That's a lot like if you look at $G(\mathbb Q_p)$ and mod out by $G(\mathbb Z_p)$, which plays an important role in the theory of Hecke operators.
Jan 23, 2011 at 6:42 comment added Ben Webster I think Scott and David's answer bring this out a bit, but let me emphasize: lots of people have studied this flag variety (try googling "affine flag variety" and "affine Springer fiber"); they aren't ignoring it out of spite, or something. It's just that the affine Grassmannian is so darn interesting.
Jan 23, 2011 at 4:28 answer added David Ben-Zvi timeline score: 6
Jan 23, 2011 at 3:04 answer added S. Carnahan timeline score: 2
Jan 23, 2011 at 2:46 history asked Najdorf CC BY-SA 2.5