# Is there an analogue of theta cycles for more general mod p automorphic forms?

The theory of $$\theta$$-cycles (due to Tate, I think) and filtrations is to me a very beautiful and powerful tool in proving many statements about mod $$p$$ modular forms in more explicit and elementary manner. Is there an analogue of $$\theta$$-cycles for mod $$p$$ automorphic forms of higher rank groups? If so, is there any occasion where such theory is used in proving some interesting statements?