Timeline for K-type in discrete series representation
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jul 11, 2021 at 23:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 13, 2021 at 22:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 13, 2020 at 21:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 16, 2020 at 21:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 18, 2020 at 21:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 19, 2019 at 20:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 23, 2019 at 5:22 | comment | added | Hebe | @JimHumphreys I use the definition as in David Vogan's book "Representations of Real Reductive Lie Groups", where a real reductive Lie group $G$ with a maximal compact subgroup $K$ is defined as: (a) Its Lie algebra $\mathfrak{g}$ is real reductive; (b) the automorphisms $\mathrm{Ad}(g)$ of $\mathfrak{g}_\mathbb{C}$ are inner for all $g\in G$. (c) There is an involutive automorphism $\theta$ of $\mathfrak{g}$, which gives a decomposition $\mathfrak{g}=\mathfrak{k}+\mathfrak{p}$; (d) The map $K\times\mathfrak{p}\rightarrow G$ is a diffeomorphism. | |
| Oct 22, 2019 at 22:28 | comment | added | Jim Humphreys | @HebeL Which version of the definition (and field) are you using? | |
| Oct 22, 2019 at 11:25 | comment | added | Hebe | @JimHumphreys Thank you for your comments, professor Humphreys. I know that there are several versions of the definitions for reductive Lie groups. Actually, when I posted this question, I was not sure about it. Let me just follow the definition in Vogan's book "Representations of Real Reductive Lie Groups", and field is real number field. Also, what if using the other versions of the definitions for reductive Lie groups? For example, just a closed subgroup of $\mathrm{GL}(n,\mathbb{C})$ preserved by taking transpose. | |
| Oct 21, 2019 at 1:47 | comment | added | Jim Humphreys | It would help if you made more explicit what you mean by "reductive Lie group".(as well as what field you are working over)/ | |
| Oct 20, 2019 at 18:09 | answer | added | jorge vargas | timeline score: 1 | |
| Oct 5, 2019 at 4:51 | comment | added | Francois Ziegler | I didn’t make this an answer, because H-C’s context is slightly different: fixed infinitesimal character. If you can add how it implies what you wanted, don’t hesitate to post that as self-answer. (I haven’t thought about it.) | |
| Oct 5, 2019 at 3:26 | comment | added | Hebe | @FrancoisZiegler Thanks a lot! | |
| Oct 4, 2019 at 18:56 | comment | added | Francois Ziegler | ... and explicitly (1954, Thm 3) where it is called an “immediate consequence of the results proved in (1953)”. | |
| Oct 4, 2019 at 14:45 | comment | added | Francois Ziegler | Knapp has something along these lines in (1986, after Corollary 10.37). He points to Harish-Chandra (1953, 1966). | |
| Oct 4, 2019 at 14:34 | history | edited | YCor | CC BY-SA 4.0 |
fixed statement
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| Oct 4, 2019 at 14:27 | history | asked | Hebe | CC BY-SA 4.0 |