A fixed-point formula for the classical groups over a finite field

Louis Solomon
1965 Transactions of the American Mathematical Society  
and let gp(9, wAere the forms d>? are, for varying q, of some fixed type. Let Giq) =Oin,q,q) be the orthogonal group and let griq) be the number of elements of Giq) with an in -r)-dimensional fixed-point set. There is a formula (1.2), for each"odd prime power q, if and only if the index of E is 0 or 1.
doi:10.1090/s0002-9947-1965-0172935-2 fatcat:ucpbdp6qhveopanatwmfgsoit4