iRule or policies based redirection based on HTTPS username behind a GTM

It can be done on LTM not GTM. You can use iRule or a LTM policy. If you have more iRule in the VS, the orders of the iRules are important in terms of which one is first applied. Irule is like :

when HTTP_REQUEST {    
    switch -glob [URI::query [HTTP::uri] username] {
        "user1" -
        "user2" -
        "user3" 
        {
            pool pool123            
        }            
        "user1" -                      
        "user2" -            
        "user3"            
        {
            pool pool456                
        }
   }            
 }