  We discuss some axioms that ensure that a Hopf algebra has its simple
comodules classified using an analogue of the Borel-Weil construction. More
precisely we show that a Hopf algebra having a dense big cell satisfies the
above requirement. This method has its roots in the work of Parshall and Wang
in the case of q-deformed quantum groups GL and SL. Here we examine the example
of universal cosovereign Hopf algebras, for which the weight group is the free
group on two generators.
