  We study unitarity of lowest weight irreducible representations of rational
Cherednik algebras. We prove several general results, and use them to determine
which lowest weight representations are unitary in a number of cases. In
particular, in type A, we give a complete description of the unitarity locus
(justified in Section 5 and appendix by Stephen Griffeth), and resolve a
question by Cherednik on the unitarity of the irreducible subrepresentation of
the polynomial representation. Also, as a by-product, we establish Kasatani's
conjecture in full generality (the previous proof by Enomoto assumes that the
parameter c is not a half-integer).
