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Oct 21, 2015 at 12:25 history edited Allen Knutson CC BY-SA 3.0
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Oct 21, 2015 at 9:38 vote accept Shi Q.
Oct 21, 2015 at 9:36 history edited Shi Q. CC BY-SA 3.0
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Oct 21, 2015 at 9:20 comment added André Henriques Note that the term "affine Grassmanian" is usually reserved for a certain infinite dimensional analogs of the Grassmanians, associated to the so-called affine Lie algebras (which are themselves infinite dimensional analogs of the finite dimensional simple Lie algebras).
Oct 21, 2015 at 9:04 answer added Sebastian Goette timeline score: 5
Oct 21, 2015 at 9:03 comment added few_reps It seems to me the answer is yes to all questions : The natural map $AG_k(\mathbf R^n)\to G_k(\mathbf R^n)$ has a contractible fiber (homeomorphic to $\mathbf R^{n-k}$) and is a homotopy equivalence.
Oct 21, 2015 at 8:38 history asked Shi Q. CC BY-SA 3.0