RECENT RESULTS ON THE IMPLICATIONS OF CRYSTAL SYMMETRY AND TIME-REVERSAL

We first recall some theorems on the extrema of functions defined on a compact manifold M invariant under the action of a finite group actin g on M and blend them with Morse theory. We apply this study to functi ons on two- or three-dimensional Brillouin zones invariant under cryst al symmetry and time reversal. After recalling some facts on invariant theory, we give explicitly the general form of these functions for th e 13 arithmetic classes in two dimensions.