Timeline for Weyl group invariants in a maximal torus
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 15, 2014 at 17:33 | comment | added | Jim Humphreys | @Tom: My first comment was too offhand, but the header and question are very confusing. In an adjoint simple group there are no $W$-invariants except 1 in $T$. Maybe the question is about Weyl groups of centralizers of semisimple elements? That was worked out (for any algebraically closed field) in the 1965 IHES paper of Borel-Tits, following Chevalley's study of regular and singular elements in $T$. | |
| Jan 15, 2014 at 12:37 | comment | added | Tom De Medts | @Jim: I don't understand your implication "So under the action of W induced by conjugation only the identity element of T is invariant" in your first comment. Could you clarify this? | |
| Jan 15, 2014 at 12:35 | answer | added | Jay Taylor | timeline score: 6 | |
| Jan 15, 2014 at 12:34 | comment | added | anonymous | There was a 1 in the (n+1)st place! | |
| Jan 15, 2014 at 12:22 | comment | added | Jim Humphreys | The problem with this example is that the equivalence class of this diagonal matrix in the adjoint group PGL is the identity element. And for the odd special orthogonal group, the negative of the identity matrix is not in this group. | |
| Jan 15, 2014 at 11:59 | comment | added | anonymous | The action of the Weyl group for PGL(2) is t--->t^{-1} so indeed -1 is left invariant under the Weyl group? | |
| Jan 15, 2014 at 11:34 | comment | added | Jim Humphreys | There is some confusion here. Recall that $W$ is defined to be the normalizer of $T$ modulo the centralizer, while the centralizer is just $T$ itself. So under the action of $W$ induced by conjugation only the identity element of $T$ is invariant. Your examples are mostly incorrect. | |
| Jan 15, 2014 at 7:51 | review | First posts | |||
| Jan 15, 2014 at 7:55 | |||||
| Jan 15, 2014 at 7:45 | history | edited | anonymous | CC BY-SA 3.0 |
added 360 characters in body
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| Jan 15, 2014 at 7:34 | history | asked | anonymous | CC BY-SA 3.0 |