Classification of finite factor representations of the \((2m+1)\)-dimensional Heisenberg group over a countable field of finite characteristic
The Heisenberg groups considered in this paper are defined over an infinite algebraic extension of \(\mathbb{F}_p\). Let \(F\) be such a field; then the dual group of the additive group is no longer a one-dimensional \(F\)-module. The author announces without proofs a number of results concerning the representation theory of these groups. First of all he constructs a family of factor representations and states that this list is complete. Further he describes the decomposition of the regular representation and states the corresponding Plancherel theorem. Finally, he describes the Grothendieck group of the group algebra \(L^1(H)\cap L^2(H)\).
scientific article; zbMATH DE number 1930668