Generic Patterns for Extensions of Simple Modules for Finite Chevalley Groups

This paper describes generic patterns for the extensions between simple modules of a finite Chevalley group. A one-to-one correspondence between these extensions and the extensions between certain simple modules of the ambient algebraic group are established. It is shown that an extension appears in a principal series representation of the finite Chevalley group if and only if the corresponding extension for the algebraic group appears in a Weyl module.