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Can we see the geometric realization of $U_q(sl_2)$'s relations as Schubert Conditions?

Well, it depends what you mean; there's certainly a close link. Any $GL_N$ invariant closed subset of the product of two Grassmannians can be described as a family of Schubert varieties. Consider th …
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Richardson varieties over finite fields

The intersections of opposite Schubert cells have a very nice decomposition into products of tori and affine spaces due to Deodhar which, of course, induces such a decomposition of the Richardson. Th …
Ben Webster's user avatar
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