Timeline for Evaluations of group characters on cosets of subgroups
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2022 at 2:00 | answer | added | Christopher Ryba | timeline score: 5 | |
| Oct 16, 2022 at 13:07 | comment | added | Geoff Robinson | This does show up in existing literature. As Will Sawin says, $\chi([gH])$ will be zero unless ${\rm Res}^{G}_{H}(\chi) > 0.$ Using Frobenius reciprocity, it will be zero unless $\chi$ is an irreducible constituent of ${\rm Ind}^{G}_{H}(1).$This sort of thing comes up a lot in the study of endomorphism rings of permutation modules, for example. Also in work on Gelfand-Graev representations. | |
| Oct 16, 2022 at 3:33 | review | Close votes | |||
| Oct 21, 2022 at 3:02 | |||||
| Oct 16, 2022 at 2:12 | comment | added | Will Sawin | Summing over $h\in H$ and dividing by $|H|$ gives the idempotent projector onto the $H$-invariants, so this is the trace of the composition of $g$ with the idempotent projector onto the $H$-invariants, which can be computed in an orthonormal basis where the first $k$ vectors are a basis for the $H$-invariants as the sum of the first $k$ diagonal entries of the matrix for $g$. | |
| Oct 16, 2022 at 1:59 | history | asked | Zach H | CC BY-SA 4.0 |