Timeline for Kazhdan Lusztig Map and conjugacy classes of Weyl groups.
Current License: CC BY-SA 3.0
8 events
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| Sep 10, 2012 at 20:11 | comment | added | Jim Humphreys |
@Aswin: It's probably reassuring to check the small case of Lie type $G_2$, where the five nilpotent orbits have dimensions 0, 6, 8, 10, 12, but the six conjugacy classes in the Weyl group (dihedral of order 12) have sizes 1, 1, 2, 2, 3, 3 (or something like that).
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| Sep 9, 2012 at 18:21 | comment | added | Aswin | @David Thanks for making my question more precise. @Jim Humphreys Thanks for the answer. I did have the lie algebra $sl_n$ in mind when I posed the question (to avoid subtleties of the map not being bijective) and should have stated it explicitly. As you point out, the orbit dimensions and the number of elements in the classes don't seem to be correlated in any special way. My question was basically to know if there actually was a connection known in the literature that I had missed. | |
| Sep 9, 2012 at 18:17 | vote | accept | Aswin | ||
| Sep 9, 2012 at 17:27 | vote | accept | Aswin | ||
| Sep 9, 2012 at 18:16 | |||||
| Sep 6, 2012 at 11:26 | comment | added | Jim Humphreys | @David: I'm basically requesting a precise formulation. In particular, the direction of the "Kazhdan-Lusztig" map is fuzzy: conjugacy classes to nilpotent orbits, or the other way? Anyway, the dimensions of nilpotent orbits don't seem to be relevant here relative to the sizes of conjugacy classes, unless I'm missing something. | |
| Sep 5, 2012 at 2:15 | comment | added | David Ben-Zvi | I think Aswin is interested in the following: given the specific map from nilpotent orbits to conjugacy classes in W defined by Kazhdan-Lusztig in the paper you helpfully cite (if I recall correctly, consider a generic arc through a given nilpotent orbit and assign the monodromy data of the corresponding regular semisimple element over the corresponding fraction field), what is the size of the resulting conjugacy class as a function of the nilpotent orbit? | |
| Sep 4, 2012 at 20:26 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
added 124 characters in body
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| Sep 4, 2012 at 19:59 | history | answered | Jim Humphreys | CC BY-SA 3.0 |