First of all, I don't think you want to use the boolean form of the getSession in your servlet. Sending flase to that method will NOT return a session if one has not been created already. If this is a user first logging in they probably won't have a session already. Try this instead
Secondly, the "session" variable is already available in a jsp. It is implicitly available to all jsp's unless you specify that it should not be. You are overwriting the implicit variable when calling
HttpSession session = request.getSession();
in you jsp. Delete that line and see what happens
session = request.getSession(false);
Lastly, you don't show the url you request and the url you redirect to. If the browser does not think they are the exact same host it will not send the cookie for the session.
String name = (String) session.getAttribute("fusion.user");
String authe = (String) session.getAttribute("fusion.auth");