  Symplectic reflection algebras arise in many different mathematical
disciplines: integrable systems, Lie theory, representation theory,
differential operators, symplectic geometry. In this paper, we introduce baby
Verma modules for symplectic reflection algebras of complex reflection groups
at parameter t=0 (the so--called rational Cherednik algebras at parameter t=0)
and present their most basic properties. By analogy with the representation
theory of reductive Lie algebras in positive characteristic, we believe these
modules are fundamental to the understanding of the representation theory and
associated geometry of the rational Cherednik algebras at parameter t=0. As an
example, we use baby Verma modules to answer several problems posed by Etingof
and Ginzburg, and give an elementary proof of a theorem of Finkelberg and
Ginzburg.
