Timeline for Expressing $\sum_{g\in [G/H]}ge_Hg^{-1}\in Z(\mathbb{C}[G])$ in terms of primitive central idempotents?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Apr 12, 2019 at 6:53 | comment | added | Denise Gi | @darijgrinberg Thank you, Darij, I'll take a look. This book looks like a valuable resource to boot. | |
| Apr 12, 2019 at 5:35 | comment | added | darij grinberg | Yes, your central element is $\operatorname{Ind}_H^G\left(1_H\right)$ when regarded as a character of $G$. Indeed, look at the formula (4.1.3) in Darij Grinberg, Victor Reiner, Hopf Algebras in Combinatorics, arXiv:1409.8356v5 and set $U = 1_H$ (so that $\chi_U$ is the function that is constantly $1$). The right hand side of the formula differs from your sum in that it sums over all $g \in G$ as opposed to only over left coset representatives; but to balance this out, it is being divided by $\left|H\right|$. | |
| Apr 12, 2019 at 5:10 | review | First posts | |||
| Apr 12, 2019 at 5:43 | |||||
| Apr 12, 2019 at 5:01 | history | asked | Denise Gi | CC BY-SA 4.0 |