  Thorne introduced the notion of adequate representations as a weakening of
the big representations used by Wiles and Taylor and others. In this appendix
to Dieulefait's paper, Automorphy of Symm5(GL(2)) and base change, we show that
certain representations of SL(2,q) are adequate. This is used by Dieulefait to
prove results about Hecke eigenforms of level 1 and newforms. We also prove
some general results about adequacy for representations of finite groups of Lie
type in the natural characteristic.
