Timeline for Finite-dimensional faithful unitary representations of SL(2,Z)
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 25, 2018 at 12:20 | vote | accept | DanielHarlow | ||
| Aug 25, 2018 at 9:25 | comment | added | YCor | @UriBader thanks for noticing. I guess the smallest index of a free subgroup is 12, so this yields a 24-dimensional representation that has finite kernel, hence kernel of order $\le 2$ (I guess 2). Using a 1-dimensional representation (through $C_{12}$ that's faithful on $-I_2$, we eventually get a faithful 25-dimensional unitary representation. | |
| Aug 25, 2018 at 8:54 | comment | added | Uri Bader | Just to state the obvious: this answer describes the extra mileage you need to go for having a faithfu two dimensional unirep. Just to get a faithful f.d unirep it is a lot easier to induce one from a finite index free group... | |
| Aug 24, 2018 at 22:52 | history | answered | YCor | CC BY-SA 4.0 |