Timeline for actions of the hyperoctahedral group
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 30, 2016 at 14:03 | comment | added | Martin Rubey | In case you run across a reference, please let me know! | |
| Jan 29, 2016 at 19:50 | comment | added | Geoff Robinson | I'm sure it must, since it is natural, but I know no reference. | |
| Jan 29, 2016 at 19:36 | comment | added | Martin Rubey | Sorry, possibly I was not clear enough: what I'd be (particularly) interested in is whether this action comes up in the literature - apart from being a very enjoyable and natural example! | |
| Jan 29, 2016 at 19:00 | comment | added | Geoff Robinson | You just take an $n$-dimensional (linear) representation of $H_{n}$ as the group of all monomial matrices with non-zero entries $\pm 1$. This may be viewed as a linear representation over any field of odd characteristic. So for $p$ an odd prime, this gives a permutation action of $H_{n}$ on the $p^{n}-1$ non-zero vectors in an $n$-dimensional vector space over the field of $p$ elements. Only the identity of $H_{n}$ fixes all vectors . | |
| Jan 29, 2016 at 18:53 | comment | added | Martin Rubey | This looks very interesting! Can you say where this comes up? | |
| Jan 29, 2016 at 17:24 | history | answered | Geoff Robinson | CC BY-SA 3.0 |