Title: On Unipotent Supports of Finite Reductive Groups With a Disconnected Centre

Author: Jay Taylor

Abstract: Let $G$ be a simple algebraic group defined over a finite field of good characteristic, with associated Frobenius endomorphism $F$. In this article we extend an observation of Lusztig, (which gives a numerical relationship between a complex character of $G^F$ and its unipotent support), to the case where $Z(G)$ is disconnected. We then use this observation in some applications to the ordinary representation theory of the groups $G^F$.