Timeline for D-modules supported on the nilpotent cone
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 1, 2009 at 18:03 | comment | added | David Jordan | Hi David, Both yours and Ben's answers were very helpful, but you seem to have pointed out that my original understanding was incorrect, so I gave you the checkmark; thanks! I have been led to ask a more basic question . | |
| Nov 1, 2009 at 17:46 | vote | accept | David Jordan | ||
| Oct 31, 2009 at 21:03 | comment | added | David Jordan | yes, sorry i understand now what you said: the centralizer any non-zero nilpotent element has two components each equal to \CC. | |
| Oct 31, 2009 at 18:47 | comment | added | David Treumann | They aren't simply connected! Even for SL_2. The centralizer of [[0,0],[1,0]] has one component of the form [[1,0][,1]] and one of the form [[-1,0][,-1]]. | |
| Oct 31, 2009 at 15:11 | comment | added | David Jordan | Sorry, I think I introduced the confusion here. It should be G equivariant not g equivariant. A lot of difference a shift makes. As it was explained to me, Ben's point about the orbits being simply connected for sl_n is important here. | |
| Oct 28, 2009 at 16:36 | comment | added | David Treumann | Are lower-case-g equivariant D-modules more like imposing equivariance with respect to a simply connected group or an adjoint group? SL_n (even SL_2) has a center, so there is always some equivariant local system on the regular orbit. In SL_2, this regular orbit is topologically C x C^*, and I think that SL_2 equivariance means that the monodromy around that C^* squares to 1. I don't know what happens for GL_n or PGL_n. | |
| Oct 28, 2009 at 14:28 | comment | added | Ben Webster♦ | Are there really non-trivial local systems in the sl_n case (I knot they happen in other types)? I was under the impression that in that case the orbits were all simply connected (since the centralizer of a nilpotent is connected). | |
| Oct 28, 2009 at 6:51 | history | edited | David Treumann | CC BY-SA 2.5 |
changed notation to jibe with question. clarified and expanded.
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| Oct 28, 2009 at 3:59 | history | answered | David Treumann | CC BY-SA 2.5 |