Timeline for representation theory and finite order automorphisms
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2011 at 4:06 | comment | added | Angelo | @Jim: I wrote something wrong in my last comment, sorry you and Bruce!. I was talking only about irreducible highest weight modules and I used the term UNIVERSAL. The term universal is valid and important in another context that was on my mind, about representations of loop algebras. On the other hand, I know these modules are infinite dimensional and rarely irreducible. But I disagree that the question is out of context. | |
| Apr 1, 2011 at 13:18 | comment | added | Jim Humphreys | @Angelo: You started with "the" irreducible module (unique up to isomorphism), so "universal" is meaningless here no matter whether modules are finite or infinite dimensional. Universal highest weight modules (= Verma modules) in the BGG category are infinite dimensional and rarely irreducible. Also, "categorical" here depends on which category of modules you are working in. | |
| Mar 31, 2011 at 12:42 | comment | added | Jim Humphreys | @Angelo: I don't understand what "universal" means here. | |
| Mar 31, 2011 at 8:46 | history | edited | Bruce Westbury | CC BY-SA 2.5 |
added 112 characters in body
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| Mar 31, 2011 at 7:59 | comment | added | Bruce Westbury | I think I misunderstood the question. I have taken the liberty of making an edit which I hope makes it clearer. | |
| Mar 30, 2011 at 13:57 | comment | added | Angelo | @Bruce: Ok, I agree that it may be the answer. But are you saying the answer is negative for all $g$ of type $A_n$, $D_n$ and $E_6$? (all types that admit a non trivial automorphism) Please, clarify me why! I guess that a bit of calculation is necessary, is not it? For instance, if $g=sl_3$ what we have ? | |
| Mar 30, 2011 at 6:19 | history | answered | Bruce Westbury | CC BY-SA 2.5 |