Timeline for Is it possible to describe the ideals of the Iwahori decomposition in a loop group using generalized minors?
Current License: CC BY-SA 3.0
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| Oct 29, 2011 at 21:36 | comment | added | Ben Webster♦ | It's very easy to see that the valuations thing describes the subsets correctly in all cases (OK, maybe not easy, but not hard). I'm interested in the scheme structure (or more concretely, the ideal one gets) and whether it is reduced (radical). That's much harder to work out. | |
| Oct 29, 2011 at 20:20 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
added 110 characters in body
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| Oct 29, 2011 at 20:03 | comment | added | Peter McNamara | You probably already know this, but For G=GL_n the closures of the double Iwahori cells can be described by a set of inequalities of the form valuation of minor greater than or equal to something. This will follow from an argument using the proof idea of Smith normal form + Gaussian elimination. For general G, I expect a similar description with generalised minors. Tempting is to embed G into some GL_n and compare the IWI decompositions for G and GL_n. Maybe this will give a possibly classification dependent proof (but there should be a better way). | |
| Oct 28, 2011 at 1:49 | history | asked | Ben Webster♦ | CC BY-SA 3.0 |