Timeline for Fundamental invariants for root subsystems
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2015 at 2:51 | vote | accept | Dr. Evil | ||
| Oct 30, 2015 at 22:42 | answer | added | Peter McNamara | timeline score: 3 | |
| Oct 29, 2015 at 23:18 | vote | accept | Dr. Evil | ||
| Nov 2, 2015 at 2:51 | |||||
| Oct 28, 2015 at 23:44 | history | edited | Jim Humphreys |
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| Oct 28, 2015 at 23:43 | answer | added | Jim Humphreys | timeline score: 4 | |
| Oct 22, 2014 at 18:35 | comment | added | Dr. Evil | Thanks Jim. As you point out, there is a more appropriate way to phrase my question: Suppose $\mathfrak{l}$ is a (pseudo-)Levi subalgebra of $\mathfrak{g}$. Is there a relationship between polynomial invariants of $\mathfrak{g}$ and $\mathfrak{l}$? | |
| Oct 22, 2014 at 0:15 | comment | added | Jim Humphreys | P.S. Looking more closely at the full list of degrees, I don't see any counterexamples to your Question 1 (unlike what I recalled previously). Still, I don't see any intrinsic relationship in terms of the invariant theory. | |
| Oct 21, 2014 at 22:55 | comment | added | Jim Humphreys | No, I don't see any interesting relationship, though it might require some case-by-case study to see if patterns are being missed. Note that your $\Psi$ involves the affine Coxeter graph (or extended Dynkin diagram) from which one or more vertices and attached edges have been removed. This idea goes back to classical work of Borel and de Siebenthal. The adjective "pseudo-Levi" is sometimes applied here, including actual Levi subalgebras of parabolic subalgebras as well as others of the type you mention. | |
| Oct 21, 2014 at 20:24 | comment | added | Dr. Evil | Yes, I do mean the degrees of algebraically independent generators of the Weyl group invariants. Thanks for pointing out the negative answer. I guess a modification of Question 1 is: is there a relationship between fundamental invariants of $\Psi$ and those of $\Phi$? | |
| Oct 20, 2014 at 13:11 | comment | added | Jim Humphreys | What do you mean by "fundamental invariants"? Your notation suggests that you mean the degrees of algebraically independent generators of the Weyl group invariants. If so, a look at the table of degrees shows quickly that Question 1 has a negative answer. In your Question 2, there might well be no reasonable relationship though of course the list of degrees always starts with 2. (Note in any case that the degrees depend just on the underlying Coxeter group and not the root system.) | |
| Oct 20, 2014 at 5:17 | history | asked | Dr. Evil | CC BY-SA 3.0 |