Timeline for the character tables of irreducible representations of $SL(3,Z_q)$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 23, 2017 at 1:19 | vote | accept | Xiao-Gang Wen | ||
| Mar 11, 2017 at 21:00 | comment | added | A Stasinski | I don't think the answer is "certainly no", since the OP is about $\mathrm{SL}_3$ and Avni, Klopsch, Onn and Voll have computed the rep zeta function in this case, for residue char bigger than $3$. We may not know the exact character table, but there is no reason to expect this to be impossible to obtain (for large residue char). For all $\mathrm{SL}_n$, $n\geq 3$, the answer is certainly "no". | |
| Mar 11, 2017 at 14:23 | answer | added | Uri Bader | timeline score: 8 | |
| Mar 11, 2017 at 8:39 | comment | added | Uri Bader | This paper relates the representation counting problem to rational singularities of the moduli space of $\text{SL}$-local systems. I really recommend trying to read it. | |
| Mar 11, 2017 at 8:31 | comment | added | Uri Bader | As @JimHumphreys says below, the answer is certainly "no". So people are led to study numerical invariants. In a remarkabel recent Inventiones paper Aizenbud and Avni study the function $n \mapsto$ (the number of representations in dimension $n$) and show it grows slower than $n^{22}$. See arxiv.org/abs/1307.0371 | |
| Mar 10, 2017 at 20:57 | comment | added | Jim Humphreys | Note that the article you mention by Simpson and Frame is accessible online at cms.math.ca/10.4153/CJM-1973-049-7 | |
| Mar 10, 2017 at 19:57 | history | edited | Xiao-Gang Wen | CC BY-SA 3.0 |
added 4 characters in body
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| Mar 10, 2017 at 1:33 | answer | added | Jim Humphreys | timeline score: 4 | |
| Mar 9, 2017 at 3:44 | answer | added | Qiaochu Yuan | timeline score: 5 | |
| Mar 8, 2017 at 23:45 | history | asked | Xiao-Gang Wen | CC BY-SA 3.0 |