A BERNSTEIN-TYPE INEQUALITY FOR LOCALIZATIONS OF IWASAWA ALGEBRAS OF HEISENBERG PRO-p GROUPS

We prove a result about the possible dimensions of modules over the completed F group algebra of a Heisenberg pro-p group that are not torsion qua modules over the centre. We explain why this result is analogous to a result of Bernstein for modules over Weyl algebras in characteristic 0.