Timeline for Irreducible representations of $\mathrm{SL}_n(K)$, $K$ finite
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2020 at 10:07 | comment | added | H A Helfgott | Sure, let us assume $K$ is finite. | |
| Jan 1, 2020 at 9:18 | comment | added | Geoff Robinson | Actually, my answer was probably only valid for $K$ finite. | |
| Jan 1, 2020 at 9:08 | comment | added | Geoff Robinson | The answers must be well-documented, but I am not sure about the best references. I guess that someone like Jim Humphreys would have the answer at his fingertips.In the case that $|K| = q,$ I would expect the largest dimension simple module in the case that $\lambda^{m}$ is the trivial character to be the Steinberg module, but I am unsure about other powers of $\lambda$. | |
| Jan 1, 2020 at 8:39 | comment | added | H A Helfgott | and, for $K=\mathbb{R},\mathbb{C}$ or $K=\mathbb{F}_q$, that would be...? | |
| Dec 31, 2019 at 21:12 | comment | added | Geoff Robinson | For large enough $m$, it would be the dimension of the largest simple module of ${\rm SL}(n,K)$ which lies over $\lambda^{m}$, where $\lambda$ is the one dimension representation of $K^{\times}$ afforded by the action of $Z({\rm SL}(n,K))$ on $V$. | |
| Dec 31, 2019 at 16:04 | comment | added | H A Helfgott | So what would the dimension of the largest-dimensional representation be, then? | |
| Nov 27, 2019 at 23:05 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
Added a little clarification
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| Nov 27, 2019 at 9:59 | history | answered | Geoff Robinson | CC BY-SA 4.0 |