Timeline for Positroids and Totally Nonnegative Complex Grassmanian
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 5, 2019 at 20:47 | history | edited | Sam Hopkins |
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| Jun 18, 2014 at 16:41 | comment | added | Sam Hopkins | Sorry, clearly I meant "Schubert cells" where I said "Bruhat cells". | |
| Jun 18, 2014 at 16:11 | answer | added | David E Speyer | timeline score: 6 | |
| Jun 18, 2014 at 13:25 | review | First posts | |||
| Jun 18, 2014 at 13:28 | |||||
| Jun 18, 2014 at 13:17 | comment | added | Sam Hopkins | Generalizing the amplituhedron story to the complex case, is also, as far as I can tell, a big open question. You might be interested in some comments of Knutson on this MO question: mathoverflow.net/questions/142841/…. | |
| Jun 18, 2014 at 13:13 | comment | added | Sam Hopkins | I think the story is something like this: the decomposition of the totally nonnegative Grassmannian into matroid strata (i.e. intersection of GGMS decomposition with t.n.n. Grassmannian) is nicely behaved; e.g., conjecturally it gives a regular CW structure. While a priori these cells ought to be common refinements of $n!$ Bruhat cells, Postnikov shows that in fact they are common refinements of only $n$ cyclically shifted Bruhat cells. KLS then apply this refinement of $n$ cyclically shifted cells to the complex case and show it is also nice. | |
| Jun 18, 2014 at 13:08 | comment | added | Sam Hopkins | This paper (Positroid Varieties: Juggling and Geometry by Knutson, Lam, and Speyer) addresses the complex case: arxiv.org/abs/1111.3660. | |
| Jun 18, 2014 at 13:02 | history | asked | snaleimath | CC BY-SA 3.0 |