  The aim of the paper is to popularise nilpotent Lie groups (notably the
Heisenberg group and alike) in the context of Clifford analysis and related
models of mathematical physics. It is argued that these groups are
underinvestigated in comparison with other classical branches of analysis. We
list five general directions which seem to be promising for further research.
Keywords: Clifford analysis, Heisenberg group, nilpotent Lie group,
Segal-Bargmann space, Toeplitz operators, singular integral operators,
pseudodifferential operators, functional calculus, joint spectrum, quantum
mechanics, spinor field.
