For the p-Sylow subgroups U of the finite classical groups of untwisted Lie type, p an odd prime, we construct a monomial CU -module M which is isomorphic to the regular representation of CU 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 .
Kirillov's orbit theory provides a powerful tool for the investigation of irreducible unitary representations of many classes of Lie groups. In a previous paper we used a modification hereof, called monomial linearisation, to construct a monomial basis of the regular representation of p-Sylow subgroups U of the finite classical groups of untwisted type. In this sequel to this article we determine the stabilizers of special orbit generators and show, that for the groups of Lie type B n and D n a subclass of the orbit modules decompose the U -modules affording the André-Neto supercharacters into a direct sum of submodules. Moreover these special orbit modules are either isomorphic or have no irreducible constituent in common, and each irreducible U module is up to isomorphism constituent of precisely one of these.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.