You cannot sue the state without permission. This law is as old as the United States. The principle provides essentially that a state must waive its sovereign immunity.
Coach Mike Leach has run into this challenge when he sued Texas Tech for violating the terms of his contract. See report. Coach Leach claims the Texas Tech University violated his employment contract when they allegedly fired him for cause. The 7th Court of Appeals in Lubbock disagreed and rejected his claim. Coach Leach says he will appeal to the Texas Supreme Court. Coach Leach, as some know, is a law school graduate.
His suit is based on breach of contract. One would expect that if the state has entered into a contract, then it has waived sovereign immunity for purposes of that one contract. So, I will be interested to read this opinion when/if it becomes public.