Orbit method for p-Sylow subgroups of finite classical groups.

For the p -Sylow subgroups U of the finite classical groups of untwisted Lie type, p an odd prime, we construct a monomial C U -module M which is isomorphic to the regular representation of C U by a modification of Kirillov's orbit method called monomial linearisation. We classify a certain subclass of orbits of the U -action on the monomial basis of M consisting of so called staircase orbits and show, that every orbit module in M is isomorphic to a staircase one. Finally we decompose the André-Neto supercharacters of U into a sum of U -characters afforded by staircase orbit modules contained in M. [ABSTRACT FROM AUTHOR]