1 results
FROBENIUS–SCHUR INDICATORS FOR PROJECTIVE CHARACTERS WITH APPLICATIONS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 08 October 2024, pp. 1-8
-
- Article
-
- You have access
- HTML
- Export citation
-
Let
$\alpha $ be a complex valued 
$2$-cocycle of finite order of a finite group 
$G.$ The nth Frobenius–Schur indicator of an irreducible 
$\alpha $-character of G is defined and its properties are investigated. The indicator is interpreted in general for 
$n =2$ and it is shown that it can be used to determine whether an irreducible 
$\alpha $-character is real-valued under the assumption that the order of 
$\alpha $ and its cohomology class are both 
$2$. A formula, involving the real 
$\alpha $-regular conjugacy classes of 
$G,$ is found to count the number of real-valued irreducible 
$\alpha $-characters of G under the additional assumption that these characters are class functions.
