Is there a nice character Theory for quaternionic representations of finite groups?

By this I mean a description of the number of Quaternionic representations of a finite group in terms of Conjugacy classes/ equivalence classes of elements in G of some sort, in analogy with the real character theory in terms of conjugacy classes of real elements?

  • 3
    $\begingroup$ One thought is that it might be possible to do something along these lines if you knew how many square roots (in $G$) each element of $G$ has. But in practice, this seems an unrealistic requirement. But, for the record, an irreducible character $\chi$ of $G$ has F-S indicator $-1$ if and only if $\sum_{g \in G}(\#$ square roots of $g$ )$\chi(g^{-1}) = -|G|$). $\endgroup$ – Geoff Robinson Jan 21 '17 at 5:51

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.